against

https://www.ldoceonline.com/dictionary/hold-y...

The "with" in that example belongs to the expression "with the best of them" though.

?

It's surely a bit like arguing that "hold one's own" takes "on" or "for" because you could say "I can hold my own on a Saturday night" or "I can hold my own for as long as necessary".

"With the best of them" is a fixed expression that means "as well as anyone else". "I can hold my own with the best of them" simply means that I am rather good at holding my own. It does not suggest that I am actually standing up to or competing with "the best of them". So Bob C.'s example doesn't shed a lot of light on which preposition should be used in a case like "the challenge of holding your own with/against a fellow competitor".

That is the rather pedantic point I was trying to make. And it assumes that I interpreted Bob C.'s example the way it was meant. Which might not be the case.

Not at all. I'm merely saying that Bob's example (if it was meant the way I am assuming it was) doesn't show that "with" is a valid alternative in cases such as the ones you mentioned.

Vielleicht macht dieses Beispiel es klarer:

Jemand fragt: Was ist die Präposition für 'sich freuen'?

Antwort: 'auf', z.B. in dem Satz "Ich freue mich auf der Arbeit am meisten über Lob."

Das heißt nicht, dass 'auf' keine korrekte Präposition für 'sich freuen' ist. Ist sie. Aber in diesem konkreten Satz geht es um etwas anderes. Er ist kein Beleg für 'sich freuen auf'.