Why can I equip a sword as a demon hunter in Diablo 3 if I can't use it?

There are several attacks available to a Demon Hunter that don't require a ranged weapon to be equipped. If you build around these abilities, such as Grenades, Caltrops, Impale, Chakram, Fan of Knives, and many others (indeed, most others), you substantially expand your available weapon options and thus, the variety of stats available to you. The downside of course is that you are locked out of some skills, such as Hungering Arrow, and - especially at low levels - you might not have all the tools you need to make this work.

Most Demon Hunters won't want to use a melee weapon, but if your skill load out supports it, or you have a really awesome 1H Sword that you want to tailor your build around, the option is there.

For future reference, the following offensive abilities can be used with a melee weapon equipped:

• Grenades
• Chakram
• Impale
• Vault + Action Shot Rune
• Fan of Knives
• Spike Trap
• Companion
• Marked for Death
• Sentry
• Rapid Fire + Bombardment Rune
• Strafe + Stinging Steel Rune
• Strafe + Demolition Rune

There may be a few others, but I don't have any confirmation on them - as a rule of thumb, anything that involves replacing arrows with knives or grenades will probably work. I'm curious about the Nether Tentacles rune for Elemental Arrow personally.

Grenades are a ton of fun, so building around them isn't some crazy niche build or anything either - using a melee weapon limits your skill options in such a build somewhat, but it opens up your equipment options considerably, which is a fair tradeoff.

You still get the stat bonus adhered to that sword when you equip it. If you are close enough to your enemy, your character should auto-swing at them with that sword.