By casting Teferi's Protection in response to your own Balancing Act, you ensure that all of your own permanents phase out and are safely treated as though they don't exist when Balancing Act resolves. Because you control zero permanents on the battlefield from the perspective of the spell, the player who controls the fewest permanents is effectively you at zero. This forces each of your opponents to match that zero, compelling them to sacrifice every single permanent they currently control while your board remains completely untouched and phased out.