Who should be author in an application note
Authorship customs tend to be very field-specific, but I've never heard of discarding a co-author from a paper just for the sake of having a shorter list of authors. This sounds ridiculous: following this reasoning your supervisor could as well decide to be the sole author of the paper!

It's common in many fields to add a supervisor as co-author (usually the last one), even if their contribution is very limited indeed. However good authorship practice recommend that every co-author should have played a significant role in the paper. So in theory you are right: if anybody should be removed from co-authorship, it's the supervisor himself.

Needless to say, it's completely unethical to deprive an actual co-author of the credit.

If there is any room for argument with this strange request, I suggest the following: check a few recent issues of this journal and count for each paper the number of authors. You should be able to easily prove that papers with more than three authors are common and there's no reason to discard anybody.