The US had nuclear weapons in countries all around the USSR by the 1960s. Not just Turkey, not just missiles. Here are their overseas deployments of nuclear-armed bombers, just as an example — this doesn't include the missiles, this doesn't include ship-based weapons. It doesn't include conventional arms or refueling planes or any of the kinds of other support.

I just point this out to avoid the idea of thinking that it was one particular deployment that made the USSR uncomfortable. They were uncomfortable for a long time.

As for why they put them in Cuba, it is a really complex set of circumstances. Castro was asking them to do it, to guarantee Cuban sovereignty after a failed US invasion attempt, and the USSR felt that the number and quality of US nuclear deployments put them in a position where they could not guarantee a second-strike attack. The Turkish missiles were provocative, but only because they really could not be used for anything other than a first-strike (they were too slow to fuel to be "reactive" in any way — you could just fly over them and attack them with conventional arms). It was also part of an early 1960s jostling between Khrushchev and Kennedy (the Berlin crisis was still fresh on their minds). I wouldn't attribute it to a single, individual thing, though — a lot of things lined up for the Soviets to think that might be a good idea, and they didn't foresee it would cause a "Crisis" of the sort that it did.