
Continuity mistake: The tyres on the crotch rocket motorcycles they were riding kept changing from knobbly tyres to road slicks, back and forth depending on what terrain they were on. Easiest to see when Ethan skids on the road to avoid the white van - clear shot of slick tyres - then about 30 seconds later they're on the dirt, he skids into the old car and you can easily see that he's got off-road tyres front and back.
Answer: Ethan did not want her to kill herself. Giving her a gun would allow her to do so.