Anzuelo literally translates to "fishhook". It's an interesting and somewhat uncommon word to find in song lyrics, making it memorable.
In the context of the song, the word is used metaphorically: "Tú lanza el anzuelo y yo lo muerdo" (You cast the hook and I bite it). This vivid imagery describes being ensnared in a manipulative relationship, where one person is constantly luring the other in, despite the pain it causes.
"Julia" has the narrator listing every reason to leave, then staying anyway. He opens flat, singing "Tú dices mentiras" [You tell lies] and "Otra ficha en tu juego" [Another piece in your game]. He already knows exactly what role he's playing, and says so before the first chorus even starts.
The chorus doesn't argue with any of that. It just asks "¿Por qué no me dejas ir?" [Why won't you let me go?], aimed at someone he's already called a liar, while she's out "Cuando estás con alguien más" [When you're with someone else]. By the second verse he drops the games entirely: "Me has usado tanto que ya hasta me duele" [You've used me so much it hurts]. He's not asking her to change. He's just repeating her name until the song runs out of things to say, and does exactly that.