The Brotherhood of Steel (BoS for short) is the Terran Starship Command's main enemy, or at least the chapter lead by Elder Irons is. The Western Brotherhood tried to assassinate the Commander (Lone Wanderer) while he/she was giving a speech for the citizens of Rivet City. Naturally, the Terran Starship Command saw this as a hostile act and struck back.
The Brotherhood believes that they should be in control of all advanced technology, most notably weapons as they think outsiders are not to be trusted and not responsible enough. It is because of this that they see the TSC as a threat.