they want to control America and created the vaults(yeah, vault-tec works with the Enclave) to experiment on people and create weapons meant for killing everything
in fallout 3 liberty prime says "Better dead than red!" red referring to communism or "the Red Menace" in the Cold War and liberty prime says this as they are attacking the Enclave
the brotherhood of steel is trying to wipe the wasteland clean of any threats and especially the Enclave (and their communist plans) and when certain people seem too powerful and dangerous, it could potentially ruin any chances of rebuilding civilization.