“Q: Why do so many resources say that mammals are the dominate animals? Is there anyway bird superiority more prominent ?”
The phrase “dominant species” is fairly difficult to define because, realistically, the dominant phylum is, and has been basically forever, the arthropods. With estimates of 1 to 10 million species and population numbers that are just staggering to think about, quantitatively they are the winners by several thousand landslides made up of primarily beetles.
But I digress. When we say the Cenozoic is the “Age of Mammals” or the Devonian is the “Age of Fishes”, it’s used more in terms of which clades exploded after the previous mass extinction (or, in earlier periods, diversified with massive geologic or climatic shifts) and took over a majority of the available ecological niches during that era/period/etc.
For example, after the Late Permian decided it preferred the Earth empty and told everyone to get rekt, the way was paved for the ancestors of dinosaurs to diversify and take over - hence the Mesozoic being known as the “Age of the Reptiles”. The same thing then happened with the K-Pg extinction event (with the exception being that the Cretaceous was generally less dramatic about the whole affair), opening up those niches for the mammals to expand into and diversify through the Cenozoic.
To go off track for a hot second, it’s a very interesting cycle of extinction-diversification that happens repeatedly. The species that are most susceptible to extinction are those that are too specialized to adapt to change (looking directly at you, Ailuropoda melanoleuca). Conversely, those that are most able to survive and then take advantage of a sudden availability of niches following an extinction event are those that are generalists (in terms of range, habitat, feeding, and the like). Various populations of these generalists will then adapt into new species as they diverge from other populations in different niches, which eventually leads to each having a very specialized lifestyle as they evolve to further take advantage of the niche. This then puts them firmly in the category of “too specialized to adapt to change” and they are now susceptible to the next major shift. SUPER COOL, RIGHT???
Anyway, to get back on track, claiming any one class/phylum/order/species of species is “dominant” during a period of geologic time is reductive, biased, and does paleontology as a whole a disservice. There are so many interesting clades that are left out when people assume the whole world at the time was populated by one small set of species (where are my extinct Ordovician hexacorallian fans at, amirite). We could just as easily call the Mesozoic the Age of Ammonites, or the Age of Conifers, and be just as accurate.