Genetic problems.
Without going into the details of genetics, it can be stated that every inherited trait, however small, is coded for by one or more genes, and each gene locus may have a substantial number of variants (alleles), which accounts for the great variety observed in a given population. Any specific individual, however, has at most only two alleles per locus—one from each parent. [snip supporting quote by James C. King]
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Then one day, many centuries later, the Lord told Noah to take two canines, two felines, two equines, two pinnipedians—one male and one female each—and put them aboard the ark. The trick is, which does our ancient zoologist choose? A male kit fox and a female Great Dane? A female lion and a male alley cat? An Eohippus and a Clydesdale? Which two individuals would possess the tremendous genetic complement that their ancestors in Eden had, to enable the many species to reappear after the flood? How could Noah tell? Creationist Dennis Wagner tells us that the original kinds degenerated through inbreeding so that their offspring would "never again reach the hereditary variability of the parent" (quoted in Awbrey...). Yet the unique couple aboard the ark needed the full genetic potential of the original kind, if not more, for a vast new array of climatic and geographic niches was opened up by the flood.