They don't necessarily need them. It depends on the surfaces they are being subjected to and the types of service they are in. Some horses are also wearing shoes to correct hoof and leg issues as well. I never had shoes on my horses but I road on trails, gravel roads and in fields almost exclusively. Horses managed to survive for thousands of years without them but they weren't subjected to the burdens of weight, concrete,show jumping and rodeo before we came along.
horses hooves grow same as a fingernail..in the wild their feet (hooves) get problems such as cracks in them and such,,domesticated horses..we try to control their feet so we can ride them..so every 3 mths. or so.. we use a file.. to Level their hooves..then we put shoes on them to help keep the hooves from getting banged up and cracked..and it helps the horse walk properly. (If one hoof was to grow longer than the others..its walk and stride would be effected.. )
You got the most accurate answer from neighbor. Horses in the wild spend a lot of time moving and they don't live in pretty pastures and stalls so the hard ground pares their feet for them. There is also the fact that a horse that comes up lame probably ends up dinner for a predator. We shoe for stressful jobs like jumping, racing, etc. we also do corrective shoeing on some horses.
There are lots of reasons, as explained above. I would add that if a horse loses the use of one of its feet, it loses its main defense...the ability to run very fast. We protect their feet because a horse with a bad foot is practically useless to us, as well as the fact that we love our horses and want them to be healthy.