Poe and Kylo aren't brothers but here is the thing, they can have that dynamic in their relationship if Kylo turns out to be Leia and Han's as most of us are convinced he is. Leia seems more like an aunt to Poe and if Poe's parents died when he was young than I think she might have more or less raised him. He is great pilot like Han, he is involved in the resistant and is probably great strategist like Leia. Kylo knows he represent everything he is not. Poe is the son the Solos wished they had.
It'll be interesting to see if this beat is played at all in the trilogy.