Forgive me if this has already been asked. I understand that some aspects of this lovely language have dependencies on where and when things are used so I'm not quite sure if this question can be answered by other general questions (most of which specifically focus on when to use "me" or "I" which is not my question).
Some useless backstory: Two of my coworkers had a disagreement today about the placement of a "me" in a binary list of people. I was roped into this discussion near the end of the day and sided with one coworker that when discussing yourself via a "list" you should always list yourself last. This is the rule I was taught at a young age and have adhered to since. I tried to bring up some reference and discussion about the rule but none was found convincing enough for my coworker to conceded her point (she was obviously wrong, isn't that how discussions go?).
The piece in question is this statement. "... due to the disagreements between me and Anthony." I feel that this grammatically incorrect and it doesn't even sound right when I speak it aloud, but my coworker is dead set that in this case the use of "me" before the name is acceptable and more correct (maybe I added that aspect to her argument, I can't recall 100% at this moment in time) than the other coworkers (and my) suggestion of "Anthony and I."
So the question is (as I was really unable to google for a decent resource to explain this rule) does this rule apply to all situations in which you are part of a list or only in certain situations, and in that case - which situations does it not apply?
(forgive invalid tags please, I'm open to suggestions/edits but this not a place I frequent so I'm not quite sure what to tag this as correctly)