Arrancarme literally means "to tear out" or "to rip out." It's a strong and evocative verb that conveys a sense of forceful removal.
In this song, Luciano Pereyra uses it metaphorically in the line "De arrancarme tu amor de raíz" (To tear your love out of me by the root). This powerful imagery expresses the deep pain and difficulty of trying to remove a love that has become so deeply ingrained, making it a memorable and impactful word choice.
Pereyra spends the first verse rehearsing a lie before he says it. "Mentiría si dijera que sin ti la vida sigue igual" (I'd lie if I said that without you life goes on the same) isn't him claiming he's fine — it's him naming the exact sentence he'd have to say to pretend he is, and rejecting it in the same breath: "No me lo creería ni yo mismo tampoco" (Not even I would believe it either).
The chorus drops the pretending and just states it: "Porque aún te amo y sigo enamorado" (Because I still love you and I'm still in love). No metaphor, no dressing it up — he wants to kiss her again and wake up next to her, and says exactly that: "Lo que no haría por volverte a besar / Y a tu lado poder despertar" (What I wouldn't do to kiss you again / And to be able to wake up by your side). By the last chorus he's back to the opening line, telling the same lie to himself.