Which games are you playing? I guess it's really second nature to most of us, but there was a time when you only had keyboard input, and most old school gamers had to learn how to play FPS with a mouse and keyboard at some point. I guess this is how I would explain the transition.
You're used to using your thumbs, one for each movement. Luckily, like on gamepads, the left is still movement and the right is still looking. But on a M+K you're primarily using your index and middle fingers. Don't think of the mouse like a trigger guard, think of it like a magnifying glass on top of a map. You're moving the mouse on one plane - the table surface. The pointer on the screen (or aiming dot) moves around one plane - a circle around your body. Like you're inside a soda can.
Don't even worry about strafing if you're having trouble learning. That way you can focus on moving foward with W, or backward with S, with just your middle finger. Eventually you'll learn to sidestep and strafe, and then sooner or later you'll learn how to pie corners with a mouse just as effectively as you did with a controller.
You do pie your corners, right? If you practice doing that as well it should definitely help.