Hydras are carnivorous and have stinging cells. They will compete with fish for live food. Although they are too small to eat adult fish, I wonder if they stress hydra fish like the Neon Tetra by stinging them when they accidentally touch the hydras.
Another problem is simply that some people do not like their appearance.
However, the biggest problem comes with infestations in breeding tanks when people are trying to breed egg laying fish. The hydras eat the live food put into the tank for the baby fish; multiply quickly and eat the baby fish.
There are several ways suggested to get rid of Hydra infestations. Most of these ways would certainly kill baby fish, and there are none that I would regard as being safe with them. So if you expect hydras are going to be a problem, you should get rid of them from your breeding tank before breeding.
Ways of Removing Hydra
In a normal aquarium, the way I like best is to use fish that eat them. The most common one used is the Blue Gourami.
A temperature of 41 degrees C (106 degrees F) for three days will apparently kill hydra. It will also kill nearly all types of fish, so these would need to be removed. Some plants will survive this heat treatment.
Naturally things like Chlorine bleach will kill hydra as well as most other things. This can be used for sterilizing non living things like rocks, and has even been used successfully for destroying pests and diseases in whole aquariums. Of course it will kill any plants and fish. Considerable effort is needed to ensure that there is no residue left before living things are reintroduced.
Apart from such drastic chemicals there are a number that can be used with fish, but not with absolute safety.
Copper can be used, but maintaining the correct level is difficult in a freshwater aquarium. Also some studies suggest that many fish are more susceptible to copper than Hydra.