(I would like to apologize in advance because English isn’t my first language)
Not only is Zim considered sensitive by Irken standards, he is canonically defective. Probably the most defective Irken that ever existed. His PAK is faulty, which makes him impossible to be brainwashed or controlled by the Control Brains. But what else does a faulty Pak entail?
Well, I think Zim simply feels too much (for an Irken). His emotions aren’t controlled by his PAK.
He is capable of being kind and hyper-empathetic, yes, but he is also a narcissist who doesn’t esistate to use and abuse his teammates, even going as far as letting them die. Hell, he blew up half of Irk on purpose during Operation Impending Doom I!
His relationship with Dib is so interesting because they are nemesis bound to fight each other until one of them is finally defeated for good, and yet they are also canonically codependent, probably in the same way Zim depends on the Tallest. In fact, he fell into a deep depression both when he found out that the Tallest weren’t coming in Enter The Florpus and when Dib gave up paranormal and their rivalry in the unaired episode Mopiness of Doom.
Every emotion, good AND bad, is at 100% all the time.
Even his devotion to the Tallests is unusual for Irken standards. Other Irkens seem to obey the Tallests mostly out of fear of what would happen if they did otherwise, but Zim? The Tallests can do no wrong according to him. Even when they gave him GIR, a clearly defective SIR unit. Even when they showed him a map of the known universe, pointed at a clearly empty space and said “there’s a planet here, and you’re going to go on a really secret mission to conquer it”. Of course he believed them! The Tallests would never send Zim, the most amazing invader Irk has ever known, to die in an empty part of the universe, drifting away for all eternity!
But what I personally find most interesting is how much Zim is capable of loving, especially artificial creatures or even inanimate objects. We usually see that with how he treats GIR, but there are other examples both in the show, the movie, and the comics.
In Issue 45, Zim and Dib’s class is given the “baby assignment”. Zim ends up making GIR create a fake baby out of meat, and he pretty much imprints on it on the spot.
After the assigment ends he refuses to destroy poor Li'l Meat Man and flees to show it the world.
In Enter the Florpus not only does Zim seem to have named every single robot he created, but he is genuinely pained when Professor Membrane starts destroying them!
And let’s not forget about Lawrence, who was probably his favourite.
Last but not least, the episode Parent Teacher Night. In that episode Dib teases Zim saying that he bets that he doesn’t even know what parents are, to which Zim replies in a small voice that of course he does. We’re then shown a flashback of the moment Zim was “born”, or actually hatched out of a test tube by a robotic arm that immediately installs the PAK on his back and tells him to “report for duty”. Zim’s reaction?
In conclusion, Zim was pretty much full of feels since birth.
Also yes, his first words were “I love you”.