I think you are confusing static and dynamic states. What you are thinking of is not what happens to the volume when you increase the pressure, but what happens to the volume after you increase the pressure and then release it.
Imagine a cylinder with a very tight-fitting piston, so gas can't get past it. If you aren't pushing on the piston, the pressure inside the cylinder is the same as the pressure outside, atmospheric. If you push on the piston, the volume of gas inside the cylinder decreases as the piston goes in, and the pressure inside the cylinder increases - you can feel it pushing back against you. If you pull on the piston, the volume of gas inside the cylinder increases as the piston comes out, and the pressure decreases - you can feel the piston pulling against you (actually, you feel the atmospheric pressure trying to push the piston back into the cylinder). So as you decrease the volume, the pressure increases, and as you increase the volume, the pressure decreases.
Now once you have pushed the piston in and increased the pressure inside the cylinder (decreasing the volume according to Boyle's Law), you arrive at a situation where the pressure inside the cylinder is higher than the atmospheric pressure (I know, thank you Captain Obvious). This is where I think you are getting confused. You are right - the pressure inside is now higher and the volume would certainly like to increase, but it can't because you are holding down the piston, maintaining the pressure. When you release the piston, the volume does indeed increase, but at the same time the pressure inside decreases, all perfectly in accordance with Boyle's Law.
When you increase the pressure, the volume decreases; when you decrease the pressure the volume increases.
When you increase the volume, the pressure decreases; when you decrease the volume, the pressure increases.