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I like to think the Aizawa secretly has a bunch of badass tattoos, and that's why he wear sleeves when we see him, because we always see him in a professional setting, it's like some unspoken thing that heros shouldn't show off their tats in public, so I imagine when he's at his house he wears tank tops and shit, showing off his full sleeves to the non-existent people.
You can write or draw this if you want, this is just what my 3am brain thinks of when my insomnia kicks in