Extinction can happen abruptly. When a giant meteor struck the earth 65 million years ago, all of the dinosaurs became extinct within days, if not hours, after the impact. Yet all those species of dinosaurs took hundreds of millions of years to evolve. We humans evolved 150,000-200,000 years ago. It likely took just a few hundred or at most a few thousand years for us to evolve from our H erectus ancestor, but the birth of a species is quick, and it often happens in a remote space, and we cannot predict which existing species will give rise to a new one. Our ancestor for example first evolved 1.8 million years ago. Yet not until 150,000-200,000 years ago did we evolve from that ancestor. What kind of people can predict exactly when should evolve from that ancestor? It could have happened earlier, later, or not at all, because evolution is unpredictable. Therefore it is trying to find a new species evolving from an existing one is extremely difficult and unlikely. First, we need to be able to predict where, when and which existing species is likely to give rise to a new one, and second, we need to live long enough to observe the entire process from start to finish. Even if someone were to live 1.8 million years, he would have to look at all populations of our own species all of the time in order to observe the speciation process. Besides, even if someone can do that, they may still come up empty handed because our ancestor could have become extinct without giving rise to a new one.
That is why we do not observe new species evolve. Take for example, the evolution of new species that came into existence after the last ice age. For example, the desert pupfish lives in desert pools in Death Valley, California, and yet this area was a glacial lake during the last ice age, which ended 13,000 years ago. People who lived 13,000 years ago may see the emptying of the lake when the ice age ended, but they won't be able to see the fish change into a new species, unless they have a longevity of at least a few hundred or thousand years. Yet because we know the desert pupfish could not have existed when the area was not a desert, we can pretty much conclude that it evolved since the end of the last ice age. Exactly how long that process took place (e.g. a few decades, a few hundred years, or a few thousand years) we do not know for sure. People only live a few decades, and people who lived in the past when medical science was less advanced live even shorter lives. To expect them to observe (if they actually did) and recognize that a species has evolved and to record it (since writing has not yet been invented) for us is simply unrealistic. Yet there is no doubt that the fossil record and other evidence such as DNA suggest that evolution is real. If you try to hide your head in the sand and deny evolution simply because no one has observed the evolution of a new species from an old one in real time, then you are just deceiving yourself.