The answer to this question can be found in Chapter 11 of Guns, Germs, and Steel. Diamond says we know that these diseases must be the oldest because they they were the ones "we could evolve and sustain..when the total human population was tiny and fragmented." Thus they were the only ones that could survive and develop among early people. The epidemic diseases, which require large, dense populations to to sustain their development, could not have existed when all of humanity lived as hunter-gatherers. Aside from their slow spread, these diseases also carry the benefit (from the perspective of the germ, of course) of not leaving survivors immune from future outbreaks. Also, because the disease takes more time to kill, people can carry it around much longer, which allows it to be spread even among widely dispersed populations.
Source: Diamond, Guns, Germs, and Steel, 204.