Do you think evolutionists derived their theory from the life cycle of a frog?
No. The theory of evolution was not derived from the life cycle of a frog. It was derived from a large body of evidence that consists of numerous and varied findings. However, in a sense, the life cycle of a frog does reiterate its past evolution. It has genes that ancestrally were those of its fish ancestors, but which have been modified through evolution to take part in its transformation into an amphibian. So, in that aspect, the life cycle of a frog provides further evidence for evolution. Added: In response to your statement about reproduction. Actually, evolution occurred before sexual reproduction came on the scene. However, with the advent of sexual reproduction the evolutionary process was enhanced. It led to the potential for greater variety because of the combining and shuffling of genes from two individuals, thus resulting in offspring that could have combined traits.