Why does the Toffoli gate output c XOR (a AND b) instead of just a AND b? The Toffoli gate takes in three inputs and gives out three outputs, and is often referred to as the quantum AND gate.

It takes in a,b,c and gives out a, b, c XOR (a AND b).

Why does it do that, instead of just giving out a,b,b AND c?  or a,b,(a AND b)?
As the comments said, if it worked like i asked, it would neither be reversible, nor a unitary matrix.

Both things are required for quantum computing!