Winning the Under Hook battle from half guard is an important part of controlling the position.
As the bottom player, your sweep game opens up, submissions, and escapes are all possible with that under hook.
As the top player, it always you to easily flatten your opponent and passing becomes much easier.
BUT, it is not everything. In fact, sometimes I like it when they get the under hook, because I can use this sneaky pass we call the Fantasma Pass – the Ghost Pass in Spanish.