It's well known by now to anyone who's played that House hates the BOS and wants them out of the way. But what we don't know is what the BOS thinks of House. We know what he believes they think about him, but that's different. All his data is from Elijah's BOS, which is outdated by the time of the game. McNamara is far more open to negotiation, as evidenced by the truce that can be signed with the NCR. Even Hardin would rather go after the Van Graffs than House, leading to the assumption they are not nearly as hostile to House as he thinks.

On a side note, what do you think the BOS would do if they knew just who House was? The single man most responsible for their beloved technology. Certainly that alone would be enough for them to offer him membership and ease tensions don't you think? Or would it make the Brotherhood even more likely to see House as a threat and attack him?

I don't see too much with this. House wants the BoS out of the way, because they attack his Securatrons, he is unsure of their capability which of course means they are a threat, and they do not fit into his overall plan for New Vegas as they are Technophiles.