The Universe exists, period. End of discussion. "Why does it exist?" is a pointless question; because there is no answer. Why can't you divide a number by zero? Because you can't divide by nothing. It's a mathematical impossibility.
If you ask me, personally, what I think of the origin of the Universe, I will probably suggest a thought experiment that goes as follows:
If we look back in time to the theoretical Big Bang singularity, we will find that space contracts, and time, being relative to space, slows down. So as time slows down and we approach the event horizon, the laws of physics begin to break down. What this means is that there is no way to measure or quantify when or how the Universe began. In short, there never was a beginning. The Universe has always existed. There never has been nothing. So the question of "Why is there something rather than nothing?" is unanswerable.