When you download a debian-based iso file (and ubuntu, thus ubuntu-mate, is debian-based), generally speaking i don’t think you want to use unetbootin to prep a usb-stick. The way i prepare a useb-stick to boot a debian-based iso file is to use dd. For example if the usb-stick is on /dev/sdb i would use,
sudo dd if=/myIsoFile of=/dev/sdb bs=10M
That command (always check the manpage before you run some command a stranger suggests) copies the iso file onto /dev/sdb using a 10-meg buffer. It’s been maybe two years since this became something of a “preferred method” of preparing a usb stick, and there are numerous websites that describe it. In any case, i’ve used it to prepare a dozen or so usb sticks for installs and i’ve never had trouble with it. I’m not 100% sure but i think there was a dd command update a while back that made the new simpler approach possible.
Good luck, if you still can’t get the iso to boot let us know, somebody will be able to figure out something.