How come the fossils in the rock strata show that while one group of species suddenly died out, another suddenly sprang into being?
What exactly are you referring to?
How is that possible? Let us see your evidence.
I will answer you if I can, if you can give me enough information about your premise, but with the following caveats:
1. I am not an evolutionary biologist, paleontologist, geologist, or in any other way a specialist. My views don't represent the state of the science in any case, but my own personal understanding. You are likely better off reading Wikipedia if you are genuinely curious, or for that matter, a decent book on the subject, which given my experience with creationists thus far, seems unlikely.
2. I will only put as much effort into answering as you evince in asking. I'm not going to spend hours of my time trying to suss enough information from an ambiguous single sentence full of misconceptions and easily discredited falsehoods just to satisfy an answer that you weren't actually looking for in the first place. Ultimately, I don't care what nonsense you choose to believe if you insist on believing it.
3. Evolutionary theory does not have all the answers, nor does it claim to. It has explanations for things that we see, from which predictions can be made about what we are likely to discover in the future, and in that sense, it has been very successful. Even if you were able to stump the most knowledgeable scientist studying in the field, it wouldn't really prove much beyond the need for additional research.