Why is the sum of two consecutive odd numbers always even?

Let x equal any odd number. x + 2 will be the next consecutive odd number. The sum, 2x + 2, describes an even number because two times anything non-zero is even and adding two to that is still even.

Visualize it. An odd bunch of anything is just an even bunch with one extra thing. Two odd bunches will be two even bunches plus two extra things. That pair of extra things makes the entire bunch even.