Componer literally means "to compose" (like music) or "to fix/repair." It's an interesting word because it has multiple layers of meaning that are beautifully used in this song.
In "Libre," Diana Fuentes sings, "Que me sé componer sola" (That I know how to compose myself alone). Here, it's not just about fixing something broken, but about rebuilding oneself emotionally and finding inner strength after a difficult experience. It implies a creative act of self-restoration, making it a powerful and unique choice.
Diana Fuentes spends this song telling the person who is leaving that she will be fine, and then showing her working. "He aprendido tanto de la vida / Que me sé componer sola" (I've learned so much from life that I know how to put myself back together alone) is the whole argument, and the kite in the chorus is the image she picks to carry it: "Libre, como cometa vuelo / Atravesando el cielo" (Free, I fly like a kite, crossing the sky). A kite is loose but still tied to something, and the next line admits it — "Flotando con todo lo que me diste" (Floating with everything you gave me).
What she refuses is the bitter version. "Y no, no quiero recuerdos tristes / Ni nada que se marchite" (And no, I don't want sad memories, or anything that withers) rules it out, while "¿Cómo olvidar lo que no se puede borrar?" (How to forget what can't be erased?) concedes the memories are staying either way. She settles it with "hoy acepto que cada momento me han hecho quien soy / Y vale perdonar" (today I accept that every moment has made me who I am, and forgiving is worth it) — leaving without erasing anything.