Why does Peridot want to understand her? That's an easy one. Understanding something - or someone, as is the case here - makes them easier to deal with in every way. And Peridot, in particular, finds understanding someone to make interacting with them far more comfortable.

So, really, it was a shame that understanding others didn't come naturally to her in the slightest.

"I like it better when I understand things," Peridot finally answers, her aggravation starting to return.