Arrastrarte comes from the verb arrastrar, which means "to drag" or "to pull along." In this context, it's used metaphorically to mean "to drag someone down" or "to pull them into a difficult situation."
The singer expresses a deep internal conflict, feeling that his own struggles and flaws would negatively impact his loved one. He sings, "Te suelto para no arrastrarte" (I let you go so as not to drag you down), highlighting his self-sacrificing decision to protect the other person from his own pain and problems.
This song is a confession from someone who feels like the danger in a relationship. The singer has been told to put himself first, but he can't shake the feeling that loving this person means he has to stop fighting his own worst instincts.
He blames himself for what went wrong between them and admits that no apology, and no drink, can quiet the guilt. So he chooses to walk away, not because he stopped caring, but because he thinks it's the only way to protect her from himself.
By the end, he calls himself the reason they broke, someone who let her go so he wouldn't drag her down with him. It's a song about loving someone enough to leave, even when leaving hurts more than staying.