Animals come and go. Why are there so many kinds of animals? Why does the animal family tree change over time?
The answer is evolution. Here are some basics.
From all this comes the diversity of life. Let's make up a mammal that lives during a time when an ice age is coming. It can't handle the change. The mammal must go somewhere else or adapt. Let's say the thickness of fur varies within that population. In the new climate, the ones with thicker fur get less sick, live longer, and produce more offspring. After a few generations, thicker fur becomes the new norm because that is what gets passed on most often. The ones with thin fur don't get a chance to have many babies.
Or perhaps the animal doesn't have much fur and never has. In fact, when an occasional mutation for thicker fur has come around in the past, those animals usually die off because they get too hot. Not now. The new mutation spreads quickly once the weather changes.
Maybe some of the animals just up and leave. They go south where weather is better. Over time, this population goes through adaptations to the new environment, which is not exactly like the old one, and the population eventually has quite different traits than the original population.
So, why aren't there saber-toothed cats in your yard and woolly mammoths tromping through the park? There are two reigning theories. There was a change in weather and there was also a change in the neighborhood. About 10,000 years ago, large predators and prey in North America got some new competition. Humans had come up with the idea of weapons. Humans out-hunted the big predators just as temperatures were warming.
Sabre toothed cat skull.
Young sabre tooth tiger skull. Image from here.
Every organism is tied to other organisms and to the environment. To put this in terms we could put on bumper stickers: Nothing stays the same. All things aren't equal. You can't escape your past. New opportunities come around all the time. Hence, we get diversity and change over time.