Next Friday

Had a discussion at work Monday night. Somebody said they were doing something
next Friday. So I said, "the Friday coming up you won't be here." He said, "It's
the Friday after that." I said, "The Friday coming up is next Friday." So we
kept on going back and forth, then other people chimed in and said I was wrong.
My reasoning is, last week was last Friday, the Friday coming up is the next
Friday.
His reasoning is, the Friday coming up is this Friday, the Friday after that is
next Friday.
To me, if Friday is next in line, it's next Friday.