Can Some One Tell Me Why My Cooper Tires In This Size Are Only 7 Inches Wide But In A Nitto They Are 10.43 Inches Wide

 

I'm guessing here, but I think you read the wrong number on the tire spec for the Coopers. I just looked up the ATR in a 265/70R17 and it shows 10.7 or 10.61 depending on if it's a P or LT tire. Min rim width is 7. Maybe that's what you saw.

 

I bet you are looking at tread width and section width (the width of the entire tire).