려 들다

be out to do something (disapproving)

-(으)려 들다 describes someone setting about doing something the speaker does not welcome, and nearly every line here carries a complaint: 쟤 또 가르치려 든다 "there they go lecturing again," 이렇게 빨리 날 없애려 드는구나, 감히 나를 훈계하려 드나?, 너희가 만약 보복하려 든다면. The pushiness is in the ending, not the verb — the plain -(으)려고 하다 would be a neutral "intend to." Expect it in irritated or confrontational speech, including sageuk-style scolding (왜 남의 집에 와서 아들 행세를 하려드느냐?).

Register: irritated, disapproving