Snaping going off slightly

Hello, I've been having problems with snaping and was hoping someone could help me with this problem.

The video was recorded with my snap to point on. I was trying to place the rectangle so that its left side is in line with the half of the ellipse. I released the mouse when it says intersect, but as you can see in the video it goes slightly to the right of to the left. 

I've noticed this problem as I was designing logos and first I thought it was my mistake, but when I tried lining it again, I saw it was impossible to do so. This is really driving me crazy.. please help!