Slang for stop it, don't do that, and/or I don't want to. Contrary to the standard dictionary definition of "allow," the slang version is used to express a negative opinion and/or an unwillingness to do something.

The phrase "allow that" is used to say no to something, or express annoyance. For example, if you ask a teenager to come to the supermarket, you'll probably get "allow that" as a response, meaning they don't want to.
NetLingo Classification: Online Jargon