While diamonds are the hardest natural substance on earth, if it weren't possible to break them, we wouldn't be able to cut them to create the sparkle we love.
Gemologically speaking, what we're talking about here is hardness vs. toughness. Hardness is resistance to scratching, while Toughness is resistance to breakage.
Diamonds form in the cubic or isometric system, which means Carbon molecules align in a cube-like pattern. There are areas where if the crystal is hit just right, the stone will split cleanly-- this is called cleavage. There are also ways to chip into the stone, usually on an edge or point, leaving a curved and step-like trough. The incredible hardness of diamonds is why they take such a high polish, but they aren't as tough, so you can wear them most of the time, but you still need to be at least a little careful with them.
What happens if I damage my diamond?
Most insurance policies will cover repair or replacement if the diamond is damaged. Sometimes you are aware you've hurt your stone, and other times it is discovered during an appraisal appointment. If your ring is already insured, I will need to write a letter to the insurance company detailing the damage and estimating the replacement or repair. Depending on the depth of a chip, recutting the stone is sometimes the better choice rather than replacement, but I can help guide you either way. If this is the first appointment, I will ensure you know about the damage and notate it on the appraisal. I can also offer guidance if you'd like to repair the chip or replace the stone.
So... I shouldn't wear my diamonds all the time?
Honestly, no. For me, I typically come home from work and change my clothes, and take all my jewelry off at the same time. Everyone is different, and the setting style, your lifestyle, etc., will always come into play, but some good rules of thumb are not to wear your jewelry to bed, to the gym, or when you're doing housework or gardening as those times are when I see the most damage.