Blue and Red have a bit of a love/hate relationship. Blue hates Red for the attention he gets and is always striving to beat Red. Meanwhile, Red holds no hatred for Blue and probably doesn’t even understand why Blue hates him so much. Often times Blue’s hatred for Red may come off as unwarranted to the player. Red is usually minding his own business and trying to become a Pokémon master when, BAM Blue’s there ready to battle. Blue is always making fun of Red while the silent protagonist sits there and takes it.
Overall, I don’t think Blue truly hates Red. Blue is using Red as an outlet for the stress he feels. The stress he causes himself, by constantly trying to be the best and get attention. The stress Professor Oak causes Blue by making him feel inadequate as a grandson, and the stress of being alone in the world without the love of a mother, a love Red has. Blue is jealous of Red and may hold some resentment because of the way his grandfather recognizes Red however, he is truly incapable of hating someone who has been his companion and his only friend.
When Blue appears in the Generation II games, he mentions how Red’s “meddling” kept him from remaining the Pokémon League Champion. Blue appears to be annoyed with himself, for not being able to overcome Red, however the disdain he used to have in the original games is missing from his voice. It seems in the three years Blue has gotten over some of his jealously and their relationship was mended.