-(으)려 states an intention and 그러다 stands in for 'do that', so this describes someone in the act of intending: 나 좀 섭섭해지려 그러네 'I'm starting to feel a bit put out', 나 때문에 그만두려 그러고 'you want to quit because of me', 몇 번 처리하려 그러다 실패한 거야 'you tried to get rid of it a few times and failed'. The textbook form is -(으)려고 하다; dropping the 고 and swapping in 그러다 is the casual spoken version.