DEET, or N,N-Diethyl-meta-toluamide, acts as a strong repellant to mosquitos via an unpleasant activation of their antennal sensilla. In other words the smell puts them off.
However it has an effective range of only about an inch so uprotected, er personal bits, are prime targets for a biting
ETA: I too am a prime target. I was in Oz a few years ago and the best protection I found was a 20% DEET aerosol which you could basically cover your entire body with in under 5 seconds.
Another thing, which you may have noticed, is that DEET acts as a rather good solvent for various plastics and some synthetic fabrics. I found this out the hard way when my crand new divers watch dissolved.