(사랑을 하고) 싶다 : I want (to love) 사랑이 (하고 싶다) : To love is (what I want to do) As you can see above, object remains object, and subject remains subject. There is no grammatical twist whatsoever.

In a phrase of -고 싶다 and the verb is a transitive verb, the particle '이/가' and '을/를' are interchangeable each other. The meaning does not depend on '이/가' or '을/를', but depends on the context. Here '이/가' is used not as a subjective particle but as an auxiliary particle.