Quality has come to mean two different things:
1) The quality of an item that teaches a pet.
2) The quality of a pet in terms of its battle stats.
The two are mutually exclusive. One has no bearing on the other.
As I recall, we used to have a way of filtering item quality. But when pet battles came along, it confused people. So we eliminated it in favor of the quality filter people wanted most -- filtering their own collected pets according to their battle prowess, which you can do here
One of the reasons why we never hear people asking to restore the item quality feature is because it really doesn't matter anymore. Item quality doesn't even match the battle stat quality. For example, all of the epic item quality pets do not yield epic battle stats. So not only is it confusing, but I think most people find it irrelevant to filter by item quality.
How do the rest of you guys feel about this?