There is a fascination with living things. The pretty colors in this aquarium are an added treat. It can relax us to peek in on life and see it peacefully exist. Aquariums are not an exception. The sad news is that just like us humans they need oxygen. The difference is that in the case of aquariums, we need to pump the air into the water. The bubbling of air and the process of evaporation put moisture into the air of our homes.
In the instance of the room with the tank in this picture, that moisture elevated the humidity enough that we had mold contamination in the room that required mold remediation. Running a dehumidifier would have avoided the need for mold remediation. It is what is being done in this home going forward now that they have learned about their aquarium and high humidity.
Fish also have their activities of daily living such as producing waste products which can become a part of our indoor air environment. The bacteria and other organic contaminants can become airborne with the evaporation water. An aquarium may not be a good idea in homes with immuno-suppressed residents