I said what I said

Take this example, from a few episodes earlier, with Burnham and Tyler discussing her relationship with Sarek:

BURNHAM: I always knew I could never be who he wanted me to be. But I realised today that it goes both ways. I'll never get from him what I want, either. TYLER: That's tough. BURNHAM: It's okay. Part of me feels unburdened. TYLER: Still, I'm sorry for that other part of you. BURNHAM: Thank you. All my life the conflict inside me has been between logic and emotion. But now it's my emotions that are fighting. I think about him and I want to cry, but I have to smile. And I feel angry but I want to love, and I'm hurt, but there's hope. What is this? TYLER: It's just being human.

There are so many writerly crimes being committed here (not the least how corny and platitudinous it is), but the biggest one is that this starkly articulated catalogue of emotions has so little grounding in context. Yes, she feels a complicated mixture of love and resentment towards Sarek, that's to be expected, but there's so little detail (and by extension, genuine emotion) driving this. It feels like it could be copy-pasted from literally any troubled parent-child relationship.

When in the actual episode, Burnham discovers that Sarek, her adoptive father, capitulated to racist and xenophobic pressure from the powers that be on Vulcan to sabotage her dreams for the future in favour of his biological child - and then, when she confronts him about it, he refuses to acknowledge their shared telepathic experience of that memory, and denies that she is a member of his family because she's not his biological child (!!!!). Furthermore, she only recently discovered that she effectively shares a part of Sarek's soul because he saved her from death in the wake of another racist attack against her. This is all very, very specific relationship building! And there's vanishingly little follow-through on it in this confessional - it's very open, very emotionally forthright (the kind of thing people are referring to when they mention characters talking like they're in therapy), but there are no specific antecedents to these emotions.

Contrast this with Kira's reflections on her mother in "Wrongs Darker Than Death or Night":

SISKO: Tell me something, Nerys. If you hate her that much, why did you save her life? KIRA: Believe me, there's a part of me that wishes that I hadn't. But the fact is, no matter what she did, she was still my mother.

The situations aren't directly comparable, but this is another situation involving a character being forced to reconcile with the fact that a parental figure cannot live up to their ideals for them, and trying to process conflicting emotions about that. And it is quite blunt, as Kira tends to be, but it doesn't over-explain. There is a wealth of potential interpretation underneath "she was still my mother," and that's where the line's power comes from. And furthermore, it is built up and anticipated by the plot of the episode - both Kira's moral disgust with her mother, as well as being moved to compassion for her situation via their familial connection, are both well elaborated in the events prior to this scene.

That's a bit grimmer and more subtle than Star Trek often trades in, but for something more heartfelt, here's the end of "The Visitor":

SISKO: You okay? JAKE: How'd you know that was coming? SISKO: I guess we were just lucky this time. JAKE: You okay, Dad? SISKO: I am now, Jake. I am now.

It's very sentimental, but it's so much more competently written. It lands because of the understatement (the succinct wording in combination with the intensity of emotion in context) and because of the dramatic irony - there is a depth of meaning to Sisko's words to which we, the audience, are privy, but Jake is not, and that in itself adds to the emotional weight of the exchange, that he is shouldering this burden of knowledge for his son in the same way that his son sacrificed his life for him in another timeline. And it's the mundane, small-scale nature of the exchange, the expressions of love and relief, that contrasts with the episode's portrayal of that father-son bond as something that persists across time and space, and that emphasizes how precious those little moments are. It's set up, it's earned, and there's something going on beneath the surface.

For another example, from Voyager's "The Chute," in which Tom Paris and Harry Kim process their hellish time in a prison together:

KIM: Tom, listen to me. I, I almost killed you. PARIS: What are you saying? You're the one that kept me alive. KIM: I was ready to hit you with the pipe. Don't you remember? PARIS: You want to know what I remember? Someone saying, this man is my friend. Nobody touches him. I'll remember that for a long time.

Again, this is not particularly subtle in the emotions being conveyed, but it is rich in its meaning in ways that directly follow the thematic work of the episode. It's an expression of grace towards a friend, and one that illuminates the subtext that everybody breaks under extreme duress, but one need not be defined by one's worst moments. Not a particularly unique message, but it does work here, because - once again! - it's commentary on a relationship that is scaled to the specific events of the plot.