I’m not sure what you mean by switching the direction of the loop, could you give some more specific explanation about that?
And when I try to bind from a reverse undermount I use a bigger loop and pinch the string while pulling upwards and it still won’t grab the string, what am I doing wrong?
Thanks in advance 
Take a braintwister for example. The loop is on the side of the yo-yo facing toward you, so if you were to then lower the loop into the gap, you would see that the direction of the loop is the same as the direction of the spin of the yo-yo. This is the wrong way to bind.
Now, if you were to get out of the braintwister mount and instead mount the string in the reverse direction (a backwards braintwister, where the string loop is on the far side of the yo-yo from you), and you were to lower the loop into the gap, you’d see that the loop is in the opposite direction of the yo-yo. This is what makes for a successful backspin bind.
And as far as this reverse undermount goes, do you mean as if you were to bind from a dismounted trapeze? If that’s the case, it just sounds like you’re throwing it the wrong way. But in either case, as long as you remember that the loop should travel in the opposite direction of the spin, you should be fine.
I practiced the bind from a trapeze / reverse undermount / what you would like to call it and I used a much bigger loop than previous times and the bind worked!
Now I can perform a bind, so thanks a lot for the tips ratfacedudeguy! 
I agree with most of that great post
but I’d rather say in order to throw stronger, your arm, wrist and hand have to be totally relaxed rather than putting more strength into the throw. relaxed will definitely be faster (like a flick, just like if you snap your fingers, the finger that actually snaps is the relaxed one, not the one where you put your strength).
correct me if I’m wrong