What's the story behind their split ?

I think it was because of Axel, the things he said and did and his actions mad the other band members angry so they broke up.

I guess he did a lot of dumb things back in the day.

Read this, it is the best info I have found on it, I had just looked this up a few days ago.
AXL ROSE & GNR Articles : Kerrang!, August 21, 1999, Part A

I agree with @charlotte234s. It was probably Axl's eccentricity and high handedness that brought down the band.