why is the orthocenter of a right triangle on the vertex that is a right angle?

Answer 1

The orthocenter of any triangle is the point where the three altitudes of the triangle intersect.

In the case of a right triangle, it is on the altitude from the right angle vertex to the hypotenuse.

Answer 2

Altitudes are perpendicular to one of the sides of a triangle and pass through the vertex opposite to that line. Perpendicular lines form right angles. A right triangle has a right angle. That means that the two line segments making up that angle are perpendicular to each other, so they are altitudes. The remaining altitude (which is perpendicular to the hypotenuse) passes through the vertex of the right angle, since they are opposite of each other. All three altitudes pass through the vertex of the right angle.

(Hopefully the wording wasn't too confusing.)