Enfadoso translates to "annoying" or "bothersome." It's a less common, yet very descriptive word to express someone who is persistent in an irritating way.
In the song, the singer declares, "Yo seré el enfadoso que no te va a dejar" (I'll be the annoying one who won't leave you). He embraces this role, acknowledging that his persistence might be bothersome, but it stems from his deep affection and determination to win her over, making it an interesting and memorable word choice.
This song is all about a guy who is not taking no for an answer! He knows his love interest doesn't want to hear from him, but he's calling anyway. He's pretty sure if he goes looking for her, she won't come out, but he's going to try regardless. He even admits, "Ya me conoces, Y ya sabes que cuando te pones terca, Yo me pongo más" [You already know me, And you already know that when you get stubborn, I get more so].
He's basically saying he's going to indulge himself in the 'luxury' of her trying to avoid him. He wants to see her face, even when she's mad, because to him, "hasta enojada es perfecta" [even angry, it's perfect]. He's going to be the annoying one who won't leave her alone because, even if she doesn't admit it, he's the one who loves her the most. He's even going to enjoy the 'luxury' of her not wanting his kisses or confirming her disdain when he tries to hug her. He's confident she'll have to deal with him "De lunes a domingo y querrás también volver" [From Monday to Sunday and you'll want to come back too]. He's ready to beg "una vez, Otra vez y otra vez" [once, Again and again]. It's a bold, persistent declaration of love!