I used to do this. Also taught spinning and weaving. For those who don't know: angora is the type of sweater that looks really hairy and is super soft.
The rabbits are not killed and skinned, they are either plucked or shorn. (Never, ever pluck a rabbit when the fur is not ripe... it hurts terribly!) I sheared mine because the wool stays denser and finer than it does if you pluck. There is a book about it and the authors compared the two methods... it was quite striking. (Too lazy to walk upstairs, turn on the lights and look for that book right now, but it was written by two ladies and for a long time was the only book to be found about this.)
Let me tell you, keeping rabbits in shape for proper shearing is a lot of work. You have to groom them all the time. You will need to carefully comb out the coat, or you will get mats in the wool. The wool grows, on average, about an inch a month. This means three to four shearings per year. (Depending on the staple length you are aiming for.) Don't let either the grooming or the shearing go; you will regret it, and the rabbit will suffer. Believe me, the people who go through this earn the money they charge.
One of the best deals I ever had was when I raised English Angoras and sold them as pets. Many of the owners did not want to bother with shearing, so they brought the rabbits back to me for that. I would shear and clean them up, clip toenails etc. Most of the time they did not want the wool. (To be honest, it was not always in great shape, but there was some useable wool in there.) So I sold the rabbit, and then got paid to shear it, and sometimes had useable wool to sell.
There are different breeds of Angora and they all have their quirks. For example the French Angora has a different type of coat than the English. I always fed my rabbits on the best pellet I could get, as well as very good quality hay. Don't scrimp on feed for a fiber animal; they can not grow good fiber if they don't have good feed.
Shearing requires you to be very careful; a rabbit's skin is like tissue paper, and you don't want to nick them. You must be patient and work *with* the rabbit. Usually they are very good-natured about it but can become very sensitive depending where you are shearing. This is where all that work on grooming comes in! Hopefully they have learned to trust you. Take your time and give the rabbit a break every now and then. With practice, you can get pretty fast... but, a rabbit would take me close to 45 minutes to shear, whereas I could shear an alpaca in about 15 minutes... so remember, it takes a lot of time.