Cyprus is only in due to blackmail [/simplified, but not much].
How was it blackmail?
At numerous times during the many years of preparation of the Big Eastward Expansion, Greece (usually subtly) threatened that they'd veto any major eypansion that didn't also include (South) Cyprus.
What makes things more complex is, of course, that South Cyprus had to make some pretty serious efforts at reunification as part of the price of getting in. Though timing and smallprint made it so that in the end they had the choice between getting in together with the North or without it, with sadly predictable outcome (whatever you think of the Annan plan's merits)
You are right, that IS oversimplification.
First, Cyprus has one of the healthiest economies in Europe. So that made the EU willing to (partly) turn a blind eye to the territorial disputes with Turkey.
Secondly, I wish we had so much leverage as to blackmail France, Germany and the UK for anything, let alone EU expansion. Actually, if we had that much power perhaps we'd have persuaded by now the Europeans to be more forceful towards Turkey about the EU customs union.