We had known that birds are descended from dinosaurs well before the general public and the majority of paleontologists starting saying “birds are dinosaurs”. So simply saying that “we discovered that birds are descended from dinosaurs” is not sufficient to answering your question.

Traditional taxonomy allows for paraphyletic groups, meaning that not all of the descendants of the most recent common ancestor of the group are required to be in that group. So in this case, even though it was known that birds are descended from dinosaurs, they continued to be considered two separate groups, with dinosaurs being a paraphyletic group. Birds were known first, dinosaurs were later discovered and were considered a distinct group, then the link between the the two groups was discovered, but how they were grouped did not immediately change. That birds were not considered to be dinosaurs was a rather arbitrary effect based on how they were discovered and not on any scientific basis.

One book on dinosaurs from 1997 wrote:

In a phylogenetic sense, dinosaurs are not extinct, for birds are theropodan descendants (but see Feduccia 1996 for a dissenting view). For the purposes of this review, however, the term dinosaur connotes what cladists might term “non-avian dinosauromorph.” We thus (unrepentantly) use a paraphyletic rather than monophyletic (holophyletic) “Dinosauria.” Whatever the scientific merits of the latter, the former is widely understood, and avoids such circumlocutions as “non-avian dinosaur.”

A later edition of that same book from 2012 not only uses “non-avian dinosaur” extensively, it also has an entire section on birds.

So why the change? There is a trend in science to prefer cladistic classification, which requires every group to be a clade, meaning that all descendants of the most recent common ancestor of a group are in the group. This effectively means that paraphyletic grouping is being abandoned. So with cladistic taxonomy birds are dinosaurs.

There are other traditionally paraphyletic groups that are still in the process of changing. For example traditionally monkeys were a paraphyletic group, but any clade that includes all monkeys necessarily includes the apes, so in cladistics apes are monkeys. Though, you will still hear many people say ‘apes are not monkeys’. Fish was also a paraphyletic group, which included all vertebrates except tetrapods, but of course in cladistics, tetrapods are fish.

The idea is quite old:

Shortly after the 1859 publication of Charles Darwin’s On the Origin of Species, the British biologist Thomas Henry Huxley proposed that birds were descendants of dinosaurs. He compared the skeletal structure of Compsognathus, a small theropod dinosaur, and the “first bird” Archaeopteryx lithographica (both of which were found in the Upper Jurassic Bavarian limestone of Solnhofen). He showed that, apart from its hands and feathers, Archaeopteryx was quite similar to Compsognathus.

But having fossil evidence is quite young:

One of the earliest discoveries of possible feather impressions by non-avian dinosaurs is a trace fossil (Fulicopus lyellii) of the 195–199 million year old Portland Formation in the northeastern United States. Gierlinski (1996, 1997, 1998) and Kundrát (2004) have interpreted traces between two footprints in this fossil as feather impressions from the belly of a squatting dilophosaurid.

https://en.wikipedia.org/wiki/Feathered_dinosaur

Jurassic Park in fucking 1993 has a scene where Alan Grant messes with an annoying kid, and he clearly tells the audience that they are similar to God damn birds, you silly goose. You are that kid in the film in real life.