Palabreo is a colloquial term that refers to 'sweet talk' or 'smooth talk', often used to persuade or charm someone. It implies a skillful use of words, sometimes with a hint of manipulation or flattery.
In the song, Sech sings, "La Buchana' me sacó el palabreo" (The Buchanan's brought out my sweet talk). He's implying that after drinking, he becomes more articulate and perhaps more daring in what he says, using his words to express his true feelings or to try and win back his ex, even if he's a bit drunk.
A boomerang is the thing you throw away that comes back, and Sech spends this song refusing to be one. The chorus defines the object first, "Que lo tiran y regresan, mami, no" (the kind you throw and it comes back, baby, no), then bolts the door: "Si vuelves, que no sea pa' donde mí" (if you come back, don't come back to me). He files the breakup as a returns policy. "Lo que no me queda, se devuelve" (what doesn't suit me gets returned), and by his accounting she went back a long time ago.
What stops this being a clean exit is how hard he is working at it. There is a replacement, "Tengo otra pa' no extrañarte tanto" (I have someone else so I don't miss you so much), and there is whisky doing the talking, "La Buchana' me sacó el palabreo" (the Buchanan's loosened my tongue), which is when the pettiness arrives: "No soy lindo pero con el que sales está bien feo" (I'm not handsome, but the guy you're dating is really ugly). That jab is small and funny in a way the rest of the song pretends not to be. He treats the hurt as medicine he picked himself, "Le echo alcohol a la herida, aunque me duela" (I pour alcohol on the wound, even though it hurts). Then the pose slips for one bar, "Tú eras mi motivación, sin motor, el avión no vuela" (you were my motivation; without an engine, the plane doesn't fly), and the whole refusal starts to sound like something he is telling himself.