If you're set to team, you're screwed. Team is permanently allied, it's totally unbreakable. Check the settings when you start a new game, on the screen where you can pick your opponents there is a line where you can set starting relations with each civ, it's not quite dead center in the screen, just above where you set difficulty. On each opponent, make sure that is set to something other than team - default should be unknown, but occasionally it glitches and sets them all to team.
If this had been a normal alliance situation, you can break the alliance on the trade screen.
