Does the veracity of the Bible hinge on its historical accuracy?

If the Bible is wrong about some kind of historical event, does that mean that the whole book should be tossed out? I mean that metaphorically. And I am exaggerating on purpose.

I single out historical events because these are the only things the Bible says that can be verified as true or false using other sources.

Here’s the thing: I am agnostic. I was raised Christian. There are times when I lean more toward believing in God and times where I lean more toward not believing in God. When I come across things like Christians claiming the earth is 6000 years old, I tend to think “that’s one of those things that pushes me in the atheistic direction”. Why? Because if the Bible says the earth is 6000 years old, and it ISN’T 6000 years old (which as far as I’m concerned, it’s not), then I guess I could doubt any other claim the Bible makes.