The fallacy, among others, they're committing is called equivocation, by the way. They use a meaning of one word one minute and another the next, when it suits them to win the confrontation.

This is why debate and talking don't actually solve problems. People can and will just do stupid shit like this in bad faith to get you to acquiesce to them or stop challenging them.

People like that need ass-beatings until they're willing to conform to the dictionary's definitions of words and the rules of debate.