I've reached "The House always wins: V" quest, which means I have to kill the Brotherhood of Steel. Unfortunately, I have Veronica with me and I also like the Brotherhood and their supply of armour and energy weapons. Can I follow the Mr. House line without destroying them? Mr. House has no speech options for this as far as I can tell. Do I have any options from here, or do I need to follow the Legion/NCR/Yes man?
House concluded that The Brotherhood of Steel, who are wholly against technology falling into the wrong hands, would not support his securitron-army controlled Vegas.
There is no way to ally with the Brotherhood or bypass the mission. Unless you use mods/console commands, you will need to either destroy the Brotherhood or support a different faction.