وعليكم السلام ورحمة الله وبركاته
In Islaam, self-defense is not just permitted; it's encouraged. Muslims are encouraged to train and become stronger. Rasoolullaah
صلى الله عليه وسلم said in a Hadeeth that a strong Mu'min is more beloved to Allaah Ta`aalaa than a weak Mu'min.
During the Khilaafah of Hadhrat `Umar ibn al-Khattaab
رضي الله عنه, he used to encourage the Muslims to train and he severely condemned obesity (as a result of overeating).
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You have read the Hadeeth but you need to understand it. Yes, in Islaam, Muslims are not supposed to hit people in the face. This is in normal scenarios. For example, you're sparring with someone, and you're punching each other in the face. This is not permissible. Another example: You go in for professional boxing, and punch people in the face and get punched in the face. Not permissible. You are causing harm to others and being dealt harm yourself, and it's uncalled for. The situation is not hostile. You are not being attacked.
If you are being attacked, on the other hand, then you can punch wherever you need to. The situation calls for it. IF you can put down the assailant without punching in the face, well and good. But if you can't, then just do what you need to do.
So it is like this: in normal, non-hostile situations, avoid punching people in the face. This is the reason boxing is not allowed in Islaam as a sport.
In a hostile situation, it's different.
والله تعالى أعلم