I recently failed to pass a skill test. I believe the examiner's decision on one of the items was incorrect, in that his advice on how to correctly fly the item directly conflicts with that given by my instructor, and my understanding of the examiner's guidance.
He cannot fail you for the wrong reasons, because it is a safety issue here.
You should know what say the SOPs, regulation, or airmanship for the situation you encountered.
Making you fail for the wrong reason might guide you to focus/learn a wrong procedure instead of improving your weakness if you have any.
The opportunity to appeal if not used is not an opportunity.
Better to get rid of this possibility if when somebody wants to appeal he fears for his career.
You have the possibility to appeal? So do it. Everybody makes mistake, and you surely more than your examiner, still, when a mistake has been done (from whoever he/she is) it has to be admited and corrected, hence the possibility to appeal.
Honestly, I know this is tricky for you, but we would be able to help you much more if you told us the item you failed and why.
If the examiner doesn't want to hear you, and if you are right (well, it's possible right?) then you have the duty to speak up because aviation is more than an ego fight between 2 persons, it is all about airmanship, honesty, rules, SOPs, safety.