Question

Why do vertices connected by a diagonal of a polygon have to be nonconsecutive?

Answer 1

Because consecutive vertices are already connected by the edges of the polygon.

Answer 2

Basically, a segment which connects two consecutive vertices is not a diagonal, it's actually a side of a polygon.

So, in order to get a diagonal, you need to unit two nonconsecutive vertices, that way you won't get a side but a diagonal.

Actually, a diagonal of a polygon is defined as a segment which connects two nonconsecutive vertices.

Therefore, by definition, a diagonal must connect two nonconsecutive vertices.