The long side of your original is 1.5x longer than the short side, which is an aspect ratio of 3:2 (8x12).
As mentioned an 8x10 (or 10x8) has a long side that is only 1.25x longer than the short side. (5:4 aspect ratio)
In other words, an 8x10 is less rectangular than the images your camera makes.
The long side of the crop you posted is 1.72x longer than the short side (1904 / 1106 = 1.722)
This edit shows an 10x8 (5:4) crop of your 3:2 aspect ratio original. (More info below edit)
The next issue is print size and quality.
To make the numbers simple we will assume a crop that leaves 1000 x 800 pixels.
At 100 pixels-per-inch (PPI) a 1000x800 pixel image will be a 10 x 8 inch print. (
1000 pixels / 100 PPI = 10 inches and
800 pixels / 100 PPI = 8 inches)
100 PPI is as low as you can go and still get a decent quality print.
A 2000 x 1600 pixel photo at 200 PPI will have better quality and will still be a 10x8 print - (
2000 pixels / 200 PPI = 10 inches and
1600 pixels / 200 PPI = 8 inches)
The way to make the pixel dimensions of the photo subjects larger in the original, so less has to be cropped, is to zoom in or get closer.
Now consider that if you don't know all this basic photograph math stuff, how can you expect the people in the photo to know it.