Why is hypotenuse longer than either 2 other legs?

One reason is that the longest side must be opposite the largest angle. Since the sum of the angles is 180 degrees, we know the other two angles together add up to 90. That is to say, we must have a right angle, 90 degrees, to have a hypotenuse, and the angle opposite the hypotenuse is the right angle.
The other two angles are smaller so the sides that are opposite from them are smaller too.