Intuition behind why rotating a point $180^\circ$ about the origin give the same result as reflecting it with respect to the origin

Question

I understand that the outcomes of those two actions could be proven mathematically, and we can see that those results match. I also understand that I can visualize those actions and see how the resultant points will end up on the same spot. However, I don't understand how those 2 actions are related as they both give rise to the same phenomenon.