1. The Brotherhood has created a empire across the Eastern US, and wants that delicious technology in MiT for its imperial ambitions.
2. The Insitute is Isolationist to the core, and may not even realize the full gravity of what the BoS empire can actually call upon.
3. The conflict between the two will form a large part of the main quest, and will be some pretty heavy shades of grey like with the Imperials and Stormcloaks.
4. A lot of callbacks to Fallout 3 stuff, banking on some Nostalgia. Fallout 3 did this with 1/2, and good old Half Life 2 had this in spades. Not something unknown to hyped up major series like this.
5. Android liberation will only be one part of the conflict. The Brotherhood won't support it out of the kindness of their hearts, but as a deliberate tactic to destabilize The Insitute and possibly gain some auxiliaries to fight alongside the power armoured elites in the final conflict and as garrisons in the new territory of Boston.