Prime angora rabbit is at least 3" long, many have fiber 4-5" long, and I've seen show English angoras with 10" long coats. I spin exclusively 100 percent pure angora, and it spins beautifully. Cotton is spun pure, and it is often under 1" in length. The problem is not the length of angora fiber, but how tightly the yarn has been spun to keep the twist, and how much the fine fiber has been damaged in processing.
Commercial angora is severely underspun, so it looks fuzzy in the ball. This yarn often lacks tensile strength and pulls apart easily. A good handspun angora has adequate twist, and doesn't fuzz out until the yarn has been worked (knitted, woven, etc.) This makes knitting easier, as you aren't fighting the fuzz. It will fluff beautifully as it is handled, and is strong enough to wear as barn mittens.
The name Angora comes from a mis-pronunciation of Ankara in Turkey. In ancient times, the long flowing coats were appreciated, and the long hair gene was encouraged in both rabbit and goat.
Angoras are not killed for their fiber, most breeds shed naturally every 3-4 months, just like a dog or cat sheds in the spring and you have handfuls of fiber flying everywhere. Some angoras were bred not to shed, so they could be sheared instead. These are often sheared every three months, giving a 3-5" fiber, similar to the length of the average sheep's wool.
The angora rabbit fiber is called 'wool' according the rabbit association. The soft fiber is an underdown, similar to cashmere, with very little guard hair. The presence of guard hair in the coat can vary; those with little or no guard hair make a very soft cashmere like yarn. Those with more guard hair, like French angora, have a very high 'spike' or fluff in the yarn, but are not as soft.
Other fiber producing animals vary in whether they use the underdown/wool, or the outer hair. Mohair from angora goats is a hair fiber, while cashmere is the underdown of a goat. Very different type of fiber. There are also breeds of sheep, which produce hair fiber instead of underdown, very useful for long wearing rugs. Some breeds have both hair and underdown, and each are used separately for different projects.
Depending on the breed, angora naturally comes in a variety of colors, similar to people's hair colors. The finer the fiber, the lighter the fiber color will be. So an angora with black hair on the face, will have gray fiber. The chocolate brown angora will have tan fiber, the fawn angora a light blonde fiber, and a red angora a peachy shade.
There are paler versions of all these colors, and some colors that have more than one color on the hairshaft (agouti), like wild rabbits do. Commercial angora is all white, and they are dyed whatever shade they want.