Why does gravity exist?

There is no reason.

It simply is.

Humans have found 4 forces that control the universe. (there many be a fifth involving quarks but that is still to be proven)

Electromagnetism

Gravity.

Strong Nuclear force

Weak nuclear Force.

Everything we experience in this universe is the interaction of these 4 forces.

I'm a decade out of school but I think you can show that any theory that allows a massless spin-2 particle necessarily gives rise to gravity as a force. I remember seeing how this exact particle emerged when solving equations of motion for bosonic string theory and being pretty impressed (iirc it was a symmetric traceless rank 2 tensor field or something similar and the Prof had to handwave a bit on it being equivalent)

So maybe we have gravity simply because there are a lot of ways to construct a universe with it and only a few special cases without it.

This is a fair question, and I doubt we've really heard the last of this subject.

The same reason why everything else exists: We Have No Idea (tm)