ok, fine, let's talk about it. first, to define a madonna-whore complex:
there are four chief opposite-sex relationships zuko has. one maternal, one sororal, one romantic, one a camaraderie. zuko's mother is his blueprint for femininity.
ursa performs values antithetical to zuko's; she cautions against treason ('not another word, young lady'), she exercises interpersonal compassion, she sees comparatively little stock in honour and status (to zuko, that is); reassuring zuko after his firebending flop, forsaking her status for the life of her son. zuko, even at thirteen, is impulsive and speaks where his tongue takes him. it takes considerable effort for compassion to be jarred from him, so deep is it buried beneath the angry exterior. zuko, until he is freed of ozai's abusive clutches, defines himself by honour, by his imperial status. that is because zuko performs masculinity, just as ursa performs femininity. on a subconscious level, he measures every girl/woman he meets against this idealised standard. and it is idealised, make no mistake, because zuko conceptualises ursa as an eternal victim who lacks total agency; just as azula does. the difference is that zuko blames azula for the victimisation of ursa, and azula blames herself (neither think to blame ozai, and that is how he likes it). zuko's dream sequence depicts ursa as frightened and calling for help within azula's dragon mouth. azula claims that even ursa 'fears' her.
where it gets interesting is when you contrast this with his perspective on azula. so, it is no secret that azula's writing -- or, rather, general portrayal -- is tinted with anti-asian racism. just as ursa is a Perfect Mother fridged in the ice of compassion, azula is... well, take a look at this:
strong? check. deceitful? 'azula always lies'... CHECK. mysterious? check. sexually alluring...? shockingly, despite her child status, check. somebody wrote a very good essay a while back on how azula's character is imbued with temptress characteristics; here, check it out: https://lokgifsandmusings.tumblr.com/post/112836094508/the-sexualization-of-azula
and, the real zinger: canonically depicted as a dragon?
so, of course, from a doylist perspective, there is a narrative bias against azula. she can't afford viewer compassion because she is sexualised, and sexualisation falls under the umbrella of adultification, and adultification is every fictional child soldier's sympathykiller. of course, that does not cover our watsonian bases.
so if ursa is the feminine ideal, it is good and right for zuko to adopt a manner that diametrically opposes hers. but for azula to be insubordinate to this expectation is... gross misconduct, in zuko's mind. this perspective is encouraged by both ozai and ursa, so he is not entirely to blame for it. zuko has been groomed into loathing azula for fear she will outperform him in every facet. zuko is the firstborn son and azula is the secondborn daughter, but she outclasses him in heirship and sonship both. she goes against her biological nature. ursa cautions azula against this too, in zuko's line of sight: she tells her to, in essence, know her place in the familial hierarchy, to speak not of the second son usurping the first. and then, of course, to appease ursa azula pretends at a family-oriented perspective: to coax zuko into 'playing' with her, she makes the claim that it is only right for brothers and sisters to spend time with one another. this kind of (largely) innocent, but repeated, deception gives way to the idea -- in zuko's mind -- that azula is unfeminine. and because she is unfeminine, she cannot be a victim of abuse. and because zuko cannot conceptualise ozai as an abuser for most of the story because it hurts his worldview, he thinks of azula as ursa's abuser.
but, in a sense, azula is also ursa's replacement. azula does unreciprocated emotional labour for zuko; she comforts him in 'the crossroads of destiny', she warns him in 'the headband', she gives him a helpful history lesson in 'the avatar and the fire lord', she leads him out of his depressive funk in 'the beach', she proposes the cathartic burning of chan's house -- in 'the beach', she reassures him in 'nightmares and daydreams', she interrupts his fumbling in 'sozin's comet's flashback in order to snatch ozai's attention away from his faultiness in a court setting. of course, azula is highly, highly emotionally and socially stunted, so a lot of this comes off as aggressive, lacking and deceitful, even if she's ~relatively~ well-intentioned. this, i think, plants the idea in zuko that all girls/women ought to be expected to perform emotional labour for him on the level ursa does (partially to compensate for ozai's lack), and somewhat explains his resentment for azula. now, to be clear, azula is not a good sister. azuls is a terrible person and this aspect is in no way absent from her relationship with zuko. but zuko does not hate her for being a terrible person. he hates her for being an obstacle; he hates that she has ozai's favour, that she is prodigious, that she is well-loved (apparently, lol, i have no idea where he got that idea from, but it's an interesting perspective-flip when you consider azula's breakdown in the finale being motivated by her self-assessment as loveless), that, perhaps, she does not play according to the rules of her birth order and sex.
okay, so, where does the 'whore' part come in? weeeelll, there are two things i would touch on here. first, zuko's dream sequence. zuko conceptualises azula as a temptress of evil; its seductive agent and his tranquiliser. the victimiser of helpless, hapless ursa. second, an interesting scene that azula-zuko dark relationship analysers have yet to dig into, perhaps because it appears so mundane in comparison:
that's. hm. that's zuko deliberately kissing his girlfriend in front of his sister.
well, i won't be coy. it's enmeshed behaviour, obviously. it's not born out of attraction; a common misconception that arises when comes to incest. it's a power play, rather. zuko is okay with kissing mai in front of azula (this is not the only time he does this, but it is the only time he does this with the deliberate purpose of... pissing azula off? or something of that like) because they don't have those kinds of (sexual) boundaries in place. because zuko presumes azula wouldn't be adversely affected by this, because she is the epitome of female sexuality; she is 'the whore'. it's a subtle brag of his own sexual/romantic monopoly in an attempt to, perhaps, incite competition. (zuko often projects his competitive feelings onto azula.)
and, of course, while we're on the topic of emotional/non-contact zucest, you'd suppose i ought to dissect the bedroom scene. well, i won't. there isn't really anything interesting to say about zuko's perspective except for the one thing -- zuko is very comfortable with eroding the boundaries between himself and a sister he hasn't seen for three years. there is nothing out of the norm, to him, in barging into her room while she sleeps, and attempting to intimidate her with the juxtaposition of his crown prince armour and her ponytail and sleeping robe. but most of the weight of the bedroom scene is in azula's perspective, rather than zuko's, and i will post about that in due course... though it likely adds to his 'whore' conception.
so ursa is the motherly madonna, and azula the sisterly whore. hey, this kind of reminds me of lannicest analysis! i did enjoy doing that. but i'll digress:
so, what of zuko's other core heterosexual relationships? that which is romantic (mai) and that which is a camaraderie (katara)? well, i don't think zuko knows how to categorise mai. initially, he conceives her as a madonna, for she has been raised to play the role of one. mai wears modest clothing and has a quiet, flat manner. even her combat style is comparatively more feminine than azula and ty lee's; mai specialises in long-range fighting, minimising direct damage. ty lee is a short-range fighter and azula is versatile. however, thanks to mai's initial lack of desire to do emotional labour for zuko, and her willingness to be an 'inconvenience' to azula extending to him and his desires, her maturity translates into sexuality (that does not centre him). by the end of 'the beach', mai resumes the role of the emotional caretaker she briefly lapsed out of, and the notion seemingly dies.
katara is zuko's fourth key opposite-sex relationship. they share a camaraderie that, from a doylist perspective, is riddled with (pseudo)romantic signifiers. like these:
incidental/flustering proximity,
touching embrace beneath the sunset; the site of zuko's date with mai.
now, do not misunderstand, i am not a zutara. i do not ship katara with anybody (except sometimes toph). but the fact is, there were zutara writers and animators in the production room, and these guys wanted to give the ship a bit of wiggle room. the narrative foilage of katara and azula lends itself to the idea of katara being zuko's 'replacement sister', especially with her defeat of azula in the final agni kai. but given how zuko's feelings towards his actual sister are not particularly... sisterly, this does not really change the aforementioned coding.
but then how does zuko, within the context of his world, view katara herself? colonial dynamics come into play here: in the earlier seasons, katara likely registers not as a man or woman but a hypersexualised 'other', thanks to her status as an indigenous victim of the fire nation's (and zuko's) genocide. zuko's 'i'll save you from the pirates' comment, and his 'big girl' comment both clearly carry a sexual undertone; hence why they were both commonly used as shipping fuel. 'the ember island players' also helps to give an insight into how the fire nation viewed water tribe women: as hypersexual yet infantile. 'katara' is depicted with a plunging neckline, a thigh slit, and a sexually provocative manner directed at 'zuko'. conversely, she ceaselessly babbles and wails, quite childishly, about her 'hope'. this is likely how zuko viewed katara in the first season: both a child and a sexual being.
however, over the course of the show, zuko's opinion of katara morphs. he begins to see her as a human being rather than a conquest in 'crossroads of destiny', and it is then that her girlhood registers. katara's parentified nature would appeal to zuko's complex, casting her as a 'madonna', but as opposed to mai, from whom emotional labour is expected, zuko is made to earn katara's trust and favour. zuko is no stranger to stubbornness; and once his mind is set on something it becomes difficult to shake. he wins her love, but again, as opposed to mai, we do not see the fallout of this, because five episodes later, the show concludes. unlike with azula, her prowess does not anger him because it's viewed as an extension of his battle for his destiny. and the 'summit' of zutara's relationship is the final agni kai, wherein katara's primary goal is not to declaw azula, but to heal zuko. healing is, within the atlaverse and our universe, a feminine art. zuko's self-sacrifice, by contrast, is masculine. to be clear, this is not to say katara, from a watsonian perspective, is 'subservient' to zuko in any way. she is absolutely not. but the narrative perspective, and zuko's perspective, claim otherwise. the agni kai ought to have been a face-off between azula and katara for the sake of azula and katara, but instead both -- but especially katara -- are reduced to their relationship with zuko.
note: the reason why i use 'narrative perspective' and 'zuko's perspective' so interchangeably is because about 50% of the atla narrative is told with an ingrained zuko bias. this will inevitably reflect upon his worldview.
zuko also interacts with toph and ty lee. it is obvious that zuko thinks of ty lee as an airheaded whore, and toph, also being a victim of colonisation, he views as an 'other' from whom emotional labour is expected but whose victimhood cannot be conceptualised.