The point of humans is misleading here: better we apply the term, speech endowed life form - which is what genesis refers to, and the factor which separates modern humans from all other life forms. The 6000 figure does not apply to any other life forms.
So you are defining humans as those who were around 6000 years ago, then concluding that humans have been around for 6000 years.
I am arguing that it has taken hundreds of thousands of years for humans to get to the point (physically and socially) where humans were 6000 years ago.
Your only evidence that humans came into existence 6000 years ago is that thats when we started writing stuff such that modern humans can read it (stone/continually rewriting/etc).
Speech endowed life forms align with what we see of modern humans within the last 6000 phase: pyramids, writings, wars, nations, names and dates - and there is no 'history' prior to the 6000.
Will you agree with me that it takes a lot more than just the ability to communicate to have pyramids, writings etc? A civilization where every member has to work all day long in order to get the food they need to survive probably can't build pyramids. They probably won't be too concerned about developing a written language when they don't have the time, nor need to read or write.
You seem to be assuming that once a being can speak that the ability and desire to write are going to happen at the same time. This is why others have cited the development of the larynx and the 40,000 plus year history of human speech.