In the molecular theory if you halve the volume without permitting the gas to heat, the molecules move at the same speed as before.
But there are twice as many molecules in any given amount of the gas so there are twice as many collisions with the walls per second.
So the pressure has doubled.
In the same way if you increase the volume while maintaining the speed of each molecule ( same temperature) you must reduce the number of collisions with the walls and hence reduce the pressure.
The kinetic theory goes a lot further because if you do compress the gas you are adding energy so the molecules would become faster and the temperature would rise,
Thus in any real compression the pressure would be a lot higher than simply calculated by boyle's law.