I really couldn't say.
The answer is just... because it was something they could think of to do... right?
ADDED: I'm told that there are some advantages to doors that open up. I'm not inclined to believe any of this, given that there are so very few cars built this way. If it's a good idea, why isn't it used more? I've got to conclude that it's just to be different. Anyway, what I'm told is that the doors take up less space and that they are less likely to open accidentally because gravity holds them down. And the DeLorean may have been designed to feed on the reputation of the the Mercedes-Benz 300SL, which is so much nicer than the DeLorean:
I like these curves so much better than the sharp angles on the DeLorean.