Opening the map defaults it to the center of the screen. If you move the map, close it, then re-open it, it will move back to it's default position.
Opening the map as the quest log does not have this same problem. That is, I can open the quest log, move it around, close it, and it is in the position I left it when I closed it.

I'm unsure what the issue would be but the two windows are virtually identical except the quest log window opens the map with the log visible.

Note: This is NOT a problem with the same version on the WoW Classic 1.13.2 (stress test) for Mac using this addon.

The error is only on the 8.2 live retail for Mac client.

This works just fine for me. The usual cause for this issue is other addons interfering with the map.

One AddOn that I know that messes with this is for example WorldQuestTracker

Ok I think I have that installed too. I'll disable it and give it a try and report back

I believe WQT might even have a setting somewhere that says something like "move map to center" or something like that.

Ok yes, under the status bar > Map Window Centralized. I unchecked that, it reloaded the UI and now the window stays where I moved it. Thanks!