just diggin into the problem: so you ran into one direction, let go of the keyboard, and the character slided further and didn't almost instantly stopped?
Or did you do a dash-attack ?
Or let me ask it in another way: When you run around, for example to the right side and then switch to run into the opposite site (to the left). Does it feel almost instant or is there a noticeable lag between you pressing the Left key (or A) and the player character going left?
He turns quickly, that's fine, he just takes a couple of extra steps before stopping when normally running. Just a fraction of a second, we can work with that.
The dash attack make a couple of extra steps so it's longer to slow down but that's momentum for you really, isn't it? Sends you off platforms too easily.