Why are there only 10,000 species of birds when there are 25,000 species of fish and 350,000 species of beetles out of at least 900,000 species of insects. A 1959 paper by G.E. Hutchinson entitled Homage to Santa Rosalia or Why are There So Many Kinds of Animals? provides some ideas.
Birds have only been around maybe 250 million years while insects came to be about 480 million years ago and fish 550 million years ago, so the latter groups have had more time to evolve as they adapted to different niches. The evolutionary history of modern groups of birds is complicated and requires a look at the fossil record, molecular data, and the morphology of extant birds. If you want to really get into the details, read Dyke and Van Tuinen’s 2004 paper, and there are many others.
Throughout the evolutionary process, habitats became more complex and provided more niches and each niche has the potential of providing for a new kind of organism. Think of a small town growing to a substantial city. The small town may have one doctor and a local car mechanic. As the town grows toward urbanization, more doctors move in, offering specialties in pediatrics, ophthalmology, and surgery while additional auto mechanics specialize in foreign or domestic car repair or electronics.
I’m oversimplifying things here, but ornithologists have known for many years that the diversity of birds is related to the structural diversity of plants. (See MacArthur’s classic paper on bird diversity.) Flowering plants evolved about the time birds did, or a bit later. Flowering plants not only provided different kinds of vegetative structure but different kinds of food as well – flowers, seeds, fruit, nectar, and provided attraction for insects. As the ecosystems become more complex, the additional niches create room for more bird species. Today we have about 10,000 living bird species and we know of thousands of extinct birds from the fossil record.
How many bird species have ever existed on earth? Estimates range from 150,000 to 1.5 million. We don’t really know because birds don’t fossilize as readily as most other animal groups. We think that, through evolutionary time a bird species would exist for about 30,000 years and that about one species would go extinct every 1000 years. Since about 1500, though, as people began to explore the world, about 500 bird species have gone extinct, or an average of one per year. Today a bird species is estimated to live for perhaps 5,000 years, about one sixth of its previous evolutionary life span. And perhaps one bird species a year goes extinct.
For a nice overview of the extinction of bird species, past, present, and future, read this Audubon article by Ken Kauffman. There is no one reason why birds get eliminated from the gene pool, there are many. These days disappearance of habitats, hunting, and invasive species are some reasons and island birds tend to be the most affected.