First of all I have to commend and thank you Sinai for conducting yourself in a professional and friendly manner, not bashing the YECs but asking them to explain themselves so that you understand (or understand why they think so).
I haven't taken a stance to being a YEC or thinking that the earth is billions of years old which is the popular belief, it doesn't really matter, what can we do about it?. I used to believe whatever they told me in school and papers about science, fortunately I know better now. Well actually that is not fortunate because it is easier to follow the crowd than to think for yourself and stand by it. Anyway, I will explain why I think YECs believe that Earth is about 6000 years old, here goes...but first I feel there are a few arguments that I should rebute....
Not really sure, but there is cave writings that does back more than 6000 years old.
Are you certain of this, is it a fact? What criteria needs to be met in your opinion if we are to call something "evidence", "fact" or even "scientificly proven". The father of a former girl friend of mine carved out a simple drawing on a big stone on the island where I live, I don't know why, as a prank or just for fun. It looked terribly like the old drawings of longboats of the Viking Era. Anyway, some people noticed it and alerted the media, scientists arrived at the scene and concluded that this was for sure viking artwork from the Viking Era (which is a 1000 years ago!). To this day it is still considered to be from the Viking Era. Scientists = fact and certainty, I think not.
How do you know? Were you there?
-Hinting to creation as the Bible depicts it.You see, this argument doesn't help your case at all because I can apply it to disprove the scientific "fact" that says the world is billions of years old.
How do you know? Were you there?. See, it works both ways. Now on to why YECs believe what they do:
It is all about priorities, should they believe the scientists that constantley prove themselves wrong, disagree widely and often have vague theories, or the Bible inspired by God and have stood the test of time and is IMO logical. Of course they would believe the latter (as do I and any christian), and if you read the Bible literally, earth was created in 6 days and man was created not long after (or so is how most people understand it, although JohnR7 mentions something about a gap), and then you just sum up the years of the generations to get a cr. number of years since creation. It is as easy as that I guess.
Edit: typo