Why is the air pressure same at all points on the inside wall of a tyre?

The short answer is: Because a gas can't support a shear stress.

In more intuitive terms: If the air pressure were different at two different points in the tire, then the air in between those two points would feel a net force; there'd be more pressure on one side of that air-in-between than on the other side. If there's a net force, then there's an acceleration, and the air would move. If the air does ever quiet down and stop having net motion--and you know from experience that it does, rather quickly--then the pressure must be the same at all points.

There actually is a small pressure difference, due to gravity, between the top of the tire and the bottom. It's a tiny fraction of atmospheric pressure, though.

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