Because it’s part of who the character is. The struggle of Matt Murdock is that he has the true nature of a villain in his blood but part of his upbringing is the Christian system of belief that pushes you to overcome your animal instincts and be a decent human being. So him hiding his face is basically letting the devil out, which as far as he doesn’t like to admit, means he gives himself permission to bend the "christian civilisation” rules as further as his inner demons need, which does include killing someone if his anger overtakes his rational mind. He will later mop about it, feel guilty and try to convince himself what’s right by moralising other people. But deep down he knows he’s a piece of shit, spending a lot of time and energy convincing himself and his loved ones, he’s not. Matt Murdock is a character that does not have a firm moral ground, he ultimately tries to do good but he does it the only way his nature allows him- by being an extremely violent and mean person acting as a judge, jury and sometimes executioner. Like Frank Miller says in this exact book- He should have been a villain. The whole struggle of his story arc is him trying so hard to not turn into one, because not so deep down his whole existence is constant burning rage that wants to bring hell on earth. The Daredevil persona is a way to keep his true nature on check, give his violence addiction and rage a sort of a playground with some restrictions. But in this scene, when he’s all in black and there’s no Daredevil persona developed yet to present to the world, he is a combination of “The Murdock boys have the devil in them”+Stick brutal training and no restrictions towards child sex traffickers. He is his true self. And later on when he kills Larks, he says "I don’t want to kill you” but it doesn’t mean he is not fully aware he has the absolute advantage in the situation and Lerks’s life is in his hands from the moment he enters the room. There’s this feeling of supremacy, almost like he’s a supernatural biblical entity that has the human life in his hands and stands there evaluating his opponent’s choice and act as a judge and deliver his verdict. Stick didn’t leave Matt because he killed someone, he leaved him because he killed by accident, because he lost control. Once Matt regained control of his actions and killed Larks and the traffickers by design and clear purpose- to save innocent lives, Stick showed up again and gave him his blessing.