I've pretty much always had cats, so it's not unusual for one of my sweaters to get a pulled loop, where a kitty has done a power take-off...or where I've snagged my watch...or snagged it on something. Those pulled loops are not pretty, but they are very, very easy to fix.
This is easily the teenciest crochet hook I've ever owned.
I'm pretty sure it is sized to make doilies for mice, but it makes an excellent sweater fixer. First, gently tug the sweater near the loop to shrink it as much as possible. Tug above and below the snag, to either side of it, and even diagonally.
Then, all you have to do is put the hook through from the wrong side of the sweater, so that the hook is sticking out on the right side of the sweater, right where the pulled loop is. Pull the snag to the wrong side of the sweater, and that is it! You've just repaired the snag by hiding it on the inside of the sweater.
You don't have to have such a teency crochet hook to do this, but the smaller the hook, the smaller the knits you can repair. Give it a try - it works great!