This "6K question" bothers me too. I have obtained a lot of radiocarbon dates that are older than 6,000 years, with some up to 11,0000 years. I have good evidence of human cultural activity, but no flood. Yet I am told everything I have found is wrong because "that's not what I believe." My facts and theories about those facts are dismissed.
Other scientists have a good mtDNA record of human dispersal from Africa going back some 70,000 years.
Given this type of information, why should the Young Earth theory be taught to students in public school science classes?