I am going to list all the possible reasons I could come up with.
I notice that, in general, the "no class balance!" people fall into two camps. One just doesn't understand the idea that a CR 10 fighter should be equal to a CR 10 wizard. They're used to thinking that Gandalf is more powerful than Boromir, and they gloss over that Gandalf is a high-CR Angel with some wizard levels, and that Boromir is just a guy with some fighter levels. This stance is understandable, given that in a lot of cases they're looking at existing stories that feature higher-level casters serving as advisors to up-and-coming warriors. Stories don't mention "character level," though, so again, the confusion is totally understandable.
.The other group is far larger, and tends to have several things in common (not always, but surprisingly often). I have a pet hypothesis that fits a lot of anecdotal data -- but not enough to be anything more than that yet:
I think these all tie together. I think reactionary people dislike change (4e, vs. Pathfinder = 3.X, which is the "original" game they're used to). I think authoritarian people need things to be "official" and to have a clear hierarchy -- Pathifinder is "officially supported" vs. 3.5 no longer being supported, so it's the go-to game. And I think that need for authority also manifests in the desire to have an all-powerful DM.
What does that have to do with class balance? Two things: 1. resistance to change (existing rules automatically = better than newer ones, so don't you dare even think about making any changes), and, more importantly, 2. the more unbalanced the game, the more a strong, authoritarian DM is needed to make it work. It's a self-reinforcing feedback loop.
I suspect the craving for strong authority and resistance to change are the real drivers here, not lack of knowledge, experience, or anything else more than peripherally pertaining to the game mechanics themselves.
So every time I hear "You need a better DM who fixes everything for you!" and "Balancing classes is impossible and leads to 4e," I add another data point.
Let me also add that I'm sure that there are people who don't fit into either of the above: maybe people who just don't have the experience or system mastery to see the imbalance, for example. Etc. But I think a lot of very "there is no imbalance" people fit more or less into one of those two areas.