Contradiction is not Refutation
In the first place contradiction is not refutation. No unsupported fact or statement has any value in argumentation. Such expressions as "I don't believe, I don't think so, I don't agree" introduce not arguments, but personal opinions.
You must, to make your refutation valuable, prove your position. Never allow your attempts at refutation to descend to mere denial or quibbling. Be prepared to support, to prove everything you say.