It's not the US they hate, nor the UK, it's western liberalism

This may be true (and then again, it may not), however, the pool of available recruits, which grows ever larger with every act of aggression against Muslims by "liberal western" governments, are not thus motivated. They are becoming radicalized by the violence they see visited upon their loved ones, their countries, and their people by these very "liberal western" governments, and that is what is making them easy prey for the real extremists.