Only literalist Christians who have no understanding of language at all and can't think for themselves (err, that would be all of the previously mentioned folks) misinterpret what the Bible actually says to claim the 6,000 year thing. The majority of people who call themselves Christian (followers of that hip and mythological dude, Jesus, whose own father concerns himself more with football apparently, than starving kids in Africa) do not think the Earth is only 6,000 years old.
The Hebrew word for "begat" (yalad) does not mean "son of". It's correct translation means "to bring forth" but in no way implies a father-child relationship. Compare Genesis 11:12, a verse that literalists take to mean that Arphaxad was the father of Salah, with Hebrews 7:9-10 in which begat clearly does not mean this since Levi isn't alive until 150 years after his "father". Begat indicates the first person was the originator of a (long) line of folks ending with the second person.