That phrase hurts my brain. I could name more.
I blame it on the human psyche and a part called the starter.
To me, if it turns over, it does that. You turn the key and the engine turns... over and over and over. The "starter" works fine but the engine wont run. What's up with that?

I get to look at all kinds of vehicles which wont go.
You know that when you take it to your mechanic (or tow it) the problem can suddenly disappear.

People and their phrases can confuse me. Communication is key.

"starts but wont run" hurts too sometimes... same reason. Your definition of that might be very different from one of your neighbors'

"Turns over but wont start" causes much less pain for some reason, though usually they all mean the same thing.