The "Why Not Both?" meme is more than a little overused when it comes to decisions between two good things, but it's the perfect answer to the question of whether you should use a controller or a mouse to play your favorite games.
Keyboards Suck for Movement, Controllers Suck for Aim The main problem is that keyboards are not analogue. A key is either depressed or it isn't.
This makes it essentially impossible to implement manual movement control for games using a keyboard. You have a walking speed and a sprinting speed, with nothing in between, and a significant amount of imprecision as a result.
That analog thumb stick on the controller lets you precisely control the velocity of your character, and it's intuitive. However, as soon as you try and use that same type of thumb stick to aim, things go south quickly.
When we look at something with our heads, we turn and snap to it. You don't slowly accelerate and decelerate your head, overshoot what you wanted to look at, and then turn back.