The orthocenter (H) is constructed by intersecting the altitudes. Let's see how this behaves as a "center" of a triangle:
Let me perturb one of the vertices a little...
Oops...it wasn't hard to move H right out of the triangle. Let's just play with the triangle and see what happens to H. I think you'll be convinced that H doesn't look like much of a "center" as far as the triangle is concerned.
Move that vertex a little more and H goes way out! Here, have a look:
If you want to play with this on GSP then use this.