In your professional life, there will be times of conflicts and disagreements. In a situation where you believe that you are right while others consider you wrong, people usually choose a way to explain themselves and sometimes use the wrong kind of attitude (anger or impatience), which goes against them.
If I were to be stuck in such kind of a situation then I would behave as calmly as possible. It is important for me to prove my point but losing my patience and composure will make others point true. Therefore, I would put my points and explanations forth backed with some statistical figures and opinions to make it more convincing.
However, in any case, people still believe that I am wrong. In such a scenario, I would ask them to give evidence of my wrongful deeds and in case any is true, I would accept it positively and promise them to work on it.
I would convince them with my positive attitude towards criticism and believe in myself to do the needful with my best competencies and determination. Nonetheless, if still, people believe that I am wrong then the only option for me would be to do my work with all the instructions given with a hope that someday they would see my work and attitude and consider it to be right.
This way I can let my work and efforts speak for me, instead of engaging in arguments and swear words.