The proteins in the latex have bonded to the powder in the gloves, and once they are airborne they go into the lungs. This is how the allergic reaction develops. Once enough of this protein-bonded powder gets breathed in, it causes the body to develop immunities and the response is like asthma or a hayfever allergy. Originally the gloves were powdered with talc, but in 1988 this was switched to corn starch which caused fewer cases of contact dermatitis. Now many are switching to oat powder, said to dry out the skin less and bind less to the proteins.
Most manufacturers offer all their gloves in powdered and unpowdered forms.
The powder is the vehicle for transferrance for the proteins, and the rate at which this happens can vary greatly between suppliers or even between batches from the same supplier. Unpowdered gloves go through a chlorine wash that should lower the level of concentration of the proteins on the surface by rinsing them away. But it doesn't stop with itchy dry skin and asthma. If exposure to the allergin continues, the reaction becomes more severe. It progresses from simple irritant contact dermatitis, to allergic contact dermatitis, to full latex allergy.