Why the hypothenuse of a right triangle must always be longer than either leg?

Depending on the interpretation of your question, there are two answers.

1. Definition. If another leg was longer, it would be called the hypotenuse.
2. If the hypotenuse were shorter than one of the legs forming the right angle, the hypotenuse would not be long enough to reach the other leg, and therefore not be a triangle at all.