You have no idea what Paris is talking about and you have no idea what you are talking about either. So lets brake this down a bit. There are 3 numbers listed for tire sizes, the first being the section width of the tread in mm. That's how wide the tires are. The second number is a percentage as it pertains to the side wall. So a 225/65 has a side wall that is 65% the height of what the tread width is, or 146.25 mm. The last number is the size of the rim diameter that those tires fit on. Usually listed in the tire specs is the recommended range for rim width. You wouldn't want to run a 265/XX/RXX on a 7" wide rim, it would be far to wide. Now looking at the listing for the Nitto Terra G2's that he listed they state an acceptable rim width of 6.5-9.0" so the 7" stock CX-5 rims would work, not the best choice but its doable.
Changing the section width and not changing the aspect ratio does change the over all diameter of the tires. The closest to matching the stock diameter would be a 245/60R17 that would have a 147mm side wall height. 60% of 245 = 147 65% of 225 = 146.25.
And No, wider tires do not always equal greater performance. As section width increases so will lateral grip up to a point but with that increase also comes a larger contact section hitting the road which requires more power to push down the road and a decrease in MPG because of it. Every car is different but at a certain point there is a "too wide" of a tire for it's own good as there is not enough power to push them and overall performance decreases because of it.
That being said, I don't think a 245 is above that line where performance suffers too much and in fact the increased lateral grip will probably be very welcome at a slight decrease in MPG.
There are a few people running the Falken wildpeaks in a 245/65R17 on 8" rims which is what I would suggest the OP to do if they don't care about speedo being off.