The point isn't that the Federation is bad. The point is that they resent the way it's so powerful and the way it is able to persuade so many other cultures to join it or adopt its values. They're nationalists -- they want to believe in the glory and power of their homeworlds and in the superiority of their homeworlds' culture and values. But there's the Federation over there, making sense and persuading cultures to join it on the basis of mutual consent, even as by this point both Quark and Garak have started to see that their cultures have major problems and need fundamental reform (even if they won't admit it to themselves yet).
Essentially it's a combination of not wanting the Federation's values to be better even as they're starting to realize that some of its values are better, and of generally wanting their homeworlds to not be drawn into the UFP's orbit even as they're starting to realize that may be necessary to save the Alpha Quadrant from the Dominion.