How to ask an editor to exclude a reviewer when the reasons are personal
There is often a standard statement/option on submission which offers the opportunity to declare possible "Conflict of interest." (CoI); not only for yourself, but also reviewers who might have some with you. To my knowledge this formulation intentionally leaves open whether the CoI derives from possible favouritism, antagonism, competing funding/research interests or other.

In my opinion as editor, I prefer actually not to know what the precise nature of the CoI is. As long as the author doesn't exclude a larger number of people this way, declaring isolated CoIs are perfectly in the remit of a typical researcher's career and should not count against you.

In rare cases, the editor might not have a choice but to take that reviewer on board, in which case they must take the CoI flag into account - sometimes you see reviews which are clearly not objective (biased in one or the other direction, doesn't matter); the review may still be informative, if that baseline bias is taken into account. 

However, I think an isolated CoI should, if at all possible, be taken into account by a serious editor, because many things can be at stake, such as funding, priority, plagiarism accusations and more. If they do not want to do that (for inscrutable reasons), you might consider changing publishing venue.