Illustrator - can't make a new file in mm

only pixels, points, picas, inches, feet, yards.

Millimeters, centimeters, and meters appear below yards on the Units menu in the New Document dialog. Could there be some reason that menus is getting cut off or failing to fit on your screen?

Beside that, have you tried resettting preferences?

Can you post a screenshot of what happens when you create a new document?
is it the same when you show the units when the rulers are on? (CTRL/CMD+R)
(right click on the rulers ribbon)

and is it the same when you you look at the properties with the artboard tool on?

see, I highlighted the units in my screenshot, and I can replace pt by mm and the system does the conversion.

You can also check your different options in the preferences panel (edit>preferences), in the unit section.
These are the units by default, they shouldn't prevent you from choosing another one further down the line.