Alright, here we go.
"I'm not going to listen to your argument anyway"
The fact that, by saying this, you point out that you're absolutely careless and that you are going to shrug off any (even the most reasonable) arguments. Saying this means you block every other person's out of the discussion, for no good reason at all.
Way down the line of destructiveness are sentences that begin with "By my principles, I'm against [subject X]". Principles are there for when one is too lazy to discuss why they are against something. It blocks any comments out, therefor drowning reason.
However, I find OP's 2 sentences very good as well. "Grow up" being able to aggrevate me increadibly.
Bonus:
As a single, most destructive word, I'd choose "no". It adheres to complaining, denying and turning down. The word "no" always has a negative impact on you, when hearing this, even when the message itself is happy. It is and carries negative thought.