Should I oppose reviewers whose results I show to be wrong? I am submitting a mathematics paper to a journal. This paper contains a section where I claim that some results made by some authors in different published articles are false. I give a counterexample to support my claim and also show where their proofs are flawed.

Should I oppose these authors as reviewers when I submit the manuscript? In this case what should I write in the “reason” section?
If possible, it is good form to contact these people a few days before you submit so they can "check" your counterexample.  Phrase your counterexample in a constructive manner v.g. avoid saying it is false but rather suggest their proof is incomplete.

If these people are reasonable, they will double check, confirm that the counterexample is valid, thank you for it, and maybe cite your own work.  If they are not reasonable you have still been gracious.

People don't like to be criticized in public - nobody likes it.  Avoid "springing a trap" that will get these people in a bad mood if they learn of your counterexample in a journal or as referee of the paper.