I agree with “remember the purpose”. It’s not ONLY about being assertive or aggressive.
Partly, it is. Your voice can be a self-defense weapon in and of itself. It can intimidate, and it can draw much needed attention. Bad guys want their victims weak, easy and quiet. Put up a fight and make noise. Make yourself not worth it. One of my instructors once talked about how, some people don’t like to think about the fact that a double block, done properly, can break the bad guy’s arm. To quote him, “it’s better than getting thrown into the back of a van”.
It’s also about keeping you breathing. When you shout, you exhale. This forces you to inhale. Not only does holding your breath kill your stamina, but it also keeps tension in your lungs. Think of your lungs like an air filled balloon. If it’s tied off and you smash (i.e., get punched in) it, it pops. If it’s not tied off and you smash it, the air blows out faster but the rubber doesn’t break.
It also engages your core. Involving your entire body into your strikes gives them more power. Think about a board break where a board is set up on two cinder blocks, and you are doing a palm strike. You set up in back stance, on your back foot, then step forward as you strike down into the board. That step puts your whole body momentum behind that strike.
The reason we do it in practice, and at my school we get graded on it, is because everything we do in class gets tighter, smaller, weaker and shorter in a real world situation, because we are scared. So everything you do in class, do it big and bold and strong and loud, so it has room to shrink and still be effective if you ever have to actually USE it.