That's what I thought in the beginning --- that I should be able to see the apparent concavity with my own eyes if Earth was concave. Because we don't see it, I discarded the concave earth theory as an utter garbage. However, one day I stumbled upon the facts according to which light itself bends. This discovery changed everything. Since light bends we are not able to see the concavity. Objects we see near the horizon at the eye level are actually located much higher than they appear to be.

edit:
added a nice illustration