Because it is in effect a treaty, ACTA would overcome many court precedents defining consumer rights as to "fair use" and would either change or remove limitations on the application of intellectual property laws.
I've always thought this old excuse for treaties abridging rights was a steaming load of crap. If you have rights, even treaties shouldn't be able to violate them. You can see today that governments deliberately use treaties to violate rights "legally." The US is masterful at this. Don't like a constitutionally guaranteed right? Infringe it by forcing a bogus treaty down some other countries' throats! This is one of the major failure points in so called liberal democracy.