Despreciaste comes from the verb "despreciar," meaning to scorn, despise, or look down upon someone. It is a strong word that conveys a deep sense of rejection and disrespect, far beyond simply ignoring someone.
In the song, the line "porque tú me despreciaste" (because you despised me) places the blame directly on the other person, describing the pain of being treated as worthless by someone once loved.
Jessi Uribe's "La Cadena Se Rompió" is a fantastic song about moving on after a breakup, and it's full of sass! The singer is basically saying, "I don't care if you don't love me anymore, and I don't care if you despise me." He makes it clear that he's not going to let anyone make a fool of him, declaring, "Te voy hacer saber que soy un hombre y que de mí no se burla así el que quiera" [I'm going to let you know that I'm a man and no one can make fun of me like that].
He's definitely not heartbroken, even if the relationship is over. He sings, "Me da lo mismo si me odias o me quieres, pues de mi parte la cadena se rompió" [It's all the same to me if you hate me or love me, because on my part, the chain broke]. He's confident that there are "Otras mejores que tú a mí me están esperando" [Other women better than you are waiting for me]. It's a blunt, fun song about reclaiming your independence and realizing you're better off without someone.