shitposting

yes, i’m a dummy… flies, mosquitoes, bats

No, you were right the first time. Avian doesn't mean "flying", but "relating to birds". Basically, dinosaurs are a big tree (the technical term is "clade") consisting of all animals that descend from a particular common ancestor (the last common ancestor of all dinosaurs). Because all birds descend from the same last common ancestor as raptors, sauropods, ceratopsia (e.g. triceratops), etc., birds are dinosaurs.

There seems to be some disagreement about the precise use of terminology in formal contexts, but I think in an informal context the term "avian" in "non-avian dinosaurs" has a comparatively clear meaning. Avians seems to point to the clade "aves", which are (in this case) the last common ancestor of all the currently living birds and all of its descendants. So non-avian dinosaurs is taking the clade of all creatures descended from the last common ancestor of all dinosaurs, and snipping off the sub-clade of those creatures descended from the last common ancestor of all birds.

Pterosaurs are among the most closely-related creatures to dinosaurs, but are not quite included. Bats are a long way removed from the clade of dinosaurs, and insects are even further away. None of these are avian, despite sharing the ability for flight.

Incidentally, you do seem to have touched upon three of the four separate times flight has evolved. Insects, birds, and bats. The fourth being pterosaurs. It's also thought that scansoriopterygidae, another family of dinosaurs, might have been able to fly (they could definitely at least glide), which would mean dinosaurs evolved flight two separate times: scansoriopterygidae and birds.