Because x/x at 0 = 0/0, which is indeterminate. But that's not the full answer.

If you are a calculus student, you might know this as a "removable discontinuity". Meaning that the pattern continues normally until that point. y = x/x basically follows the pattern of y = 1 until we get to x/x, which is just a small hole before continuing as normal.

The reason is because the limit as x/x goes to 0, which basically says "if we believe that the pattern continues normally as we get closer and closer to x = 0, then what does this pattern tell us SUPER close to 0?" goes to a finite value (1). Mathematically speaking:

Limit as x goes to 0 of x/x = Limit as x goes to 0 of 1 (we can do this because we are not technically AT 0, just really really infinitely close to it) = 1.

So there is just a small "hole" at x = 0.