Just to be clear, do you understand that I am not trying to argue that one genus can breed with another?
Your beliefs about the Ark and its contents bring up some questions. According to you there were about 16 000 genera of animals (not counting fish I assume) on the Ark. Yet if you follow
this link, select genus and click display results you will get a list of all the extant animal genera, a list which far exceeds 16,000. There were too many to count practically, so I only counted about halfway down the list and I came up with 22,066 genera. That was half the list, so multiply by two and we get over 44,000 genera. Multiply that by two and we get 88,000 individual animals And that only includes extant genera; there are also tens of thousands of fossil genera. So now you have a problem; you must either accept the true number of genera, a number which seems unlikely to fit on the Ark, or you can maintain your figure of 16,000 and accept that the current diversity of 44,000 genera arose from that. If we go with the estimate from the scholars you mention, that's approximately 7000 individuals (number of families times two). That still strains credibility, but if we accept that figure for the sake of argument, that means that we now have 44,000 genera that all arose from 7000 individuals. It doesn't matter if we use your number or the scholars you mention; the conclusion is that modern genera must be related to certain other genera because they arose from the same progenitor.
Please ask for clarification if you didn't follow that. Here's a brief summary just in case:
-You posit 16,000 genera on the Ark, there are at least 44,000 genera (not including fossil taxa) of animals today
-That many animals could not fit on the Ark, especially if we include extinct animals
-if there were only 16,000 genera on the Ark and 44,000 today, some of those 44,000 must share common ancestors among the original 16,000
-if you accept that, you have accepted the fact that one genus can eventually give rise to a new genus