If Ukraine had kept its nukes it would have been destabilizing. It was a big concern at the fall of the Soviet union about all the "loose nukes" in the unstable, newly free former members. It was wisely deemed best to not have a bunch of new (unstable) nuclear states in the club.

We keep calling it a "democracy" to invoke sentiment and sympathy. The fact is that they're quite corrupt, and them having nukes would have been foolish for Europe and everyone.