Answer:
In short, it was the courtship between two young, star-crossed lovers that caused six deaths.
Legitimate Answer:
By the end of the play, Juliet had developed her own independence away from her parents, and dare I say, she's become a bit rebellious. Romeo gains maturity and confidence out of his desire for Juliet. But Shakespeare was an ideal tragedy maker, if both had ignored their want for eahother, they'd walk away from the foolish, love-starved thoughts that clouded their heads. The main themes are loyalty, Romeo's loyalty to Juliet. Love between the two, and hate, disdain, and distrust between the two families. Greed by both families and the young Lovers themselves. Violence, in the blood and gore of the fights between the two families and in-the-middle friends, and tragedy, of course, for the deaths of Romeo and Juliet each in their own. The theme(s) was Tragedy and Insanity.
Off the record, do not include this in the answer, if you ever want to be a theater teacher, student, or any sort of writer, be it song, play, or novel, you should learn that this question is ridiculous, I mean, no offence, but Shakespeare was a playwright, and a legendary one at that, he was known for multiple themes in a single play, not singular themes for a single play. This question might as well be considered subversive.