Something impermissible isn't allowed. It's impermissible in every part of the U.S. to drive 100 miles an hour on the highway.
Things that are permissible are legal, authorized, or welcome — you are permitted to do them. The opposite of permissible is impermissible, which adds the "opposite" prefix im- to permissible, from the Latin permittere, "let, allow, grant, or permit." It's impermissible to bully other kids at school, or against the rules, and it's impermissible to steal a car, or against the law.
adj not permitted
forbidden, out, prohibited, proscribed, taboo, tabu, verboten
excluded from use or mention
unsuitable or forbidden as a topic of conversation
forbidden to the touch
intolerable, unbearable, unendurable
incapable of being put up with