Why is the pH of pure water 7?

It almost never is. BUT

(pH stands for potential hydrogen)

pH is a (negative of) the log of the number of positive ions in the water.

At 25 degrees C, thermal agitation in pure water will produce 10 to the minus 7 (moles of) ions per liter,

thus pH 7 (at 37 degrees it's 7.4)