Why does gas not liquify at a temperature above the critical temperature no matter how much pressure is applied on it? Why?
The critical point is a point of convergence of all state properties of the respective liquid and gas. It can be considered as the degeneration point, where there is no difference between gas and liquid and this distinguishing does not make sense any more.
It can be also said the supercritical fluid near the critical point is neither gas neither liquid. It is both at the same time. Farther from critical point, like for permanent gases, either gas-like either liquid-like properties are dominant, depending of the state.
By changing  pressure of supercritical fluid, it gradually transforms between  states, where it behaves more like gas or liquid, without evaporation or condensation. It is similar, as if you reach an elevated level via a big step (liquid/gas or evaporation/condensation) versus  along a slope (supercritical fluid). For the latter, there is no upstairs (gas) nor downstairs(liquid), there is just the slope.
Imagine you figurally walk as the substance on the phase diagram ($T$ grows to the right, $p$ grows upwards) around the critical point. If you do it counter-clockwise, you will evaporate as many times as many rounds you do, without ever condensing. If you do so clockwise, you will condensate as many times as many rounds you do, without ever evaporating.