Why should I let bread cool before slicing and eating?
It is because of the way starch retrogrades. It does so in stages. The first stage needs between 1 and 2 hours, the second one a few days. 

You have probably seen it more clearly in starch-thickened puddings: they thicken a bit on stovetop, but are only ready to unmold after a few hours, else they wuoldn't keep their shape. In a bread, the starch granules are the same way: right after baking, they contain too much moisture. 

Sure, if you eat the bread right away, the aroma is very good. But the texture is problematic. It gets doughy and dense at the smallest amount of pressure. Tearing instead of cutting helps a bit. And if you are at home, eating with your family, go for it and eat the tasty still-hot bread. It is especially good with soft, low-gluten breads made with AP flour with the least amount of bran (50% milling grade or even less), my grandma would say that they "melt in the mouth" when they are hot. But if you serve bread slices to guests, or want to spread something on the bread, wait for its starch to set. 

On a side note, the second stage of starch retrogradation is the reason why you should use day-old bread for crumbs for thickening, and the third stage is the one which makes bread inedible. But this goes too far away from the original question.