okay, so if Quirks are mostly / usually based on genetics . . .
hear me out on this one okay
Aizawa can erase Quirks for a short time, basically stealing the ability to use the power away from said Quirk user he is looking at. Erasure is also something that I'm pretty sure people call a "villain quirk"
Monoma can steal the base power of someone's Quirk for five minutes, hence his hero name "Phantom Thief." Copy could also be considered a "villain quirk" due to the genuinely powerful nature of it (like, what if Decay was copied? New Order???)
These two Quirks are similar in the general sense, as Aizawa steals someone's ability to use their Quirk so long as he looks at them, Monoma can steal the ability to use a person's Quirk when he touches them, but only for five minutes.
both Quirks have a limited time, and are about warping the nature of Quirks, whether by making said Quirks unavailable to the original user or simply copying / taking the ability of that Quirk from the original user and using it yourself.
at this point, i hope y'all can see where I'm going with this
but I'm still gonna say it
the idea of Aizawa and Monoma being related in some way, shape, or form is extremely entertaining to me.
like, even if Aizawa is just the cousin of Monoma's uncle or some shit, I can imagine those big-ass family gatherings being awkward as fuck, specifically because I also see Monoma as one of those people to be genuinely nice and kind to the people he loves (aka his family), but Aizawa is lurking in the corner, being the "weird uncle" and just staring Monoma down with the "I know what you did" glare but because he doesn't want to fuck up Monoma's future, he keeps silent about the constant jabs Monoma makes at Class A
come at me all you want, but I am hereby making my headcanon that Aizawa and Monoma are related due to the similarities in their Quirks and that their family gatherings are TORTURE