The 6,000 year thing is derived from counting generations and assuming the first five days of creation were literally five 24-hour days. In the NT, it is made clear that 'days' for God are not necessarily the same as human days, citing the possibility that a day could be a thousand years. Once that door is open, why not a day that is 600 million years? Mainstream Christians usually don't have a problem with an old earth, it's the young earth creationists who can't handle deep time.
I'm not anti-Christian. I'm anti-stupid.