Rehúso is the first-person conjugation of the verb rehusar, meaning "to refuse". It's a powerful and dramatic word that expresses a strong unwillingness to do something, much more forcefully than just saying "no quiero" (I don't want to).
In this emotional song, the singer is heartbroken and can't let go of his past love. He sings, "Me rehúso a borrar los recuerdos que tengo contigo" (I refuse to erase the memories I have with you), capturing his desperate and defiant feeling of holding onto the past.
This song is a full-on drama about a guy who is completely heartbroken and not ready to move on. He calls himself a "soldado caído" (fallen soldier) with a "corazón partido" (broken heart), which is a pretty intense way to describe a breakup! He's desperate to know if his ex is as sad as he is, asking her, "Dime que también lloran tus ojitos / Y se te ponen todos rojos" (Tell me your little eyes cry too / And they get all red). He wants her to admit she still thinks of him, even if she's with a new person.
He's holding on tight to the past. He refuses to delete her pictures, even though his phone is totally full: "En el cel no me queda un espacio / Y no borro tus fotos" (There's no space left on my phone / And I don't delete your photos). He's so sure she'll come back that he still has her contact saved with a heart emoji, just waiting for her call. He is convinced that he's the love of her life and that she's just pretending with her new boyfriend, telling her, "sé que soy / El amor de tu vida" (I know I am / The love of your life).