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
After all, that's what happened to the Tin Man