I suspect that in all likelihood, Data is simply under the false impression that he's incapable of forming contractions, much like he mistakenly accepts that he was created completely without emotion, when they constantly flirted with the contrary.
Once they introduced the fact that Data can dream, but was entirely unaware of it, I came to accept that he is simply a being who's unaware of his true potential, & as a result he has mistakenly presumed a few things based on whatever evidence or instruction he had.
Ultimately, it's not a mechanical problem. If he can say its or cant, then he can certainly say it's or can't. No, his problem is that when forming a sentence he accepts that he's incapable of forming a contraction within it, & therefore prevents himself from doing so. Heck, it wouldn't even be too hard to substitute cant for can't in his programming, if he so desired
Nope, his development is such that he levels in achievements like a game, & unlocks abilities, like he did with dreaming, will eventually do with contractions, & would have done with emotion, had Soong not developed the chip upgrade. Sometimes I think that emotion chip was a weak idea. It short changed a very cool potentially natural development of him coming to find emotion within himself all along
I've long been of the same opinion. Data is already pre-programmed with things like contractions and emotions -- we saw more than enough examples of both slipping through over the seven seasons -- but there are simply algorithms in place which stop him from 'recognising' these things, hence he can't (consistently) display them (although occasionally one might sneak through by accident).
Doctor Soong didn't start from the ground-up after Lore went wrong... he simply took the existing template and installed some additional Firewalls to ensure that some of Lore's worse character traits were "hidden" within the Data type, until such time as he was able to figure out how to unlock them without unleashing another Lore on the universe. What we see in the episode Brothers
is Soong effectively recalling Data because he's finally
come up with that breakthrough: the so-called 'emotion chip'. I say "so-called" because my theory is that the chip doesn't actually give
Data emotions. Rather, it simply updates his firmware while removing the restrictions on the emotions that are already built into his core. He was always capable
of emotion (re: episodes like The Naked Now
where said emotions clearly bubble to the surface), but until the 'emotion chip' was installed, those capabilities were simply locked away within his matrix. Inaccessable.