Ok, so I think Shigaraki and Uraraka are cousins. See we Kotaro's (Shigaraki's dad) side of the family but never Nao's (the mom's) side. Shigaraki's mom might have had a sibling then that sibling had Uraraka.
It would make sense that Uraraka didn't know anything about the incident because any good parent doesn't want their kid to know about something traumatizing that happened in the family. And if Uraraka knew about Nana there would be a chance that she would find out about the incident so her parents just never told her. Or her parents never knew about Nana.
Now lets look at Nao and Uraraka's mom.
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Nao
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Uraraka's mom
Now they don't look exactly a like, but most siblings don't. But first let's look at the similarities. One is that they both have brown hair, just different shades. They have close to the same face shape.
Now let's look at quirks. Uraraka's mom might be able to manipulate body parts, as we see her putting Uraraka's eye back in place. We don't know Nao's quirk. Uraraka has to place all five fingers on an object or human to remove its gravity. Now Shigaraki has to place all five fingers on an object or human to disintegrate it. Now we know that quirks are genetic. So having to place all five fingers for their quirk to activate it is suspicion.
