Why Takeoff angle is measured up from the horizon, and the steeper a wave hits the ionosphere, the harder it is to bend it back down. For a given frequency and level of ionization there is a maximum takeoff angle at which the wave still refracts back to Earth; go any steeper and it punches through into space. That limit is the critical angle, and it is the angular counterpart of the critical frequency, which is the highest frequency returned when the wave is sent straight up.
Watch out The choice naming the lowest takeoff angle inverts the idea: low, shallow angles are the easiest to return and give the longest skip distances, so there is no lower cutoff. Long path and short path azimuths are bearings in the horizontal plane, nothing to do with elevation.
Too steep and you leak through: the critical angle is the HIGHEST angle that still comes back.