Do you mean equal in terms of their area? Imagine holding your scissors at the far left edge of any shape. If you cut it there, the right piece will obviously have more area than the left. So you slide the scissors from left to right, looking for a better place to cut. If you slide too far, the scissors will end up towards the far right edge, and then the left piece will obviously have more area than the right piece.

If I can slide my scissors along a continuous path from left to right, so that in my starting position there's more area in the right piece and in the ending position there's more area in the left piece, it logically has to be true that at some moment my scissors were over the location where that transition happened - that location is a place where you can cut and have two halves of equal area!