I will most likely get secondguessed by someone but I will attempt to answer this question in case someone else is
LED here by google looking for an answer. The correct answer is yes and no. Does your dog get sick from your flu? Until bird or dog flu mutated was it able to be transmitted to humans? The answer is no, however, you can become a pathogen and vise versa with your fish.
A great example might be an infection caused by a certain type of bacteria. Say your finger had an open cut just under your fingernail, and you stuck your hand into the tank. if a fish has an infection caused by bacteria and that fish carried that bacteria over to your open cut, you could get an infection from your fish. The opposite scenario also applies and is the biggest reason behind stressing a fish, and removing slime, why you never grab a fish.
The above is also why it is an awesome idea to wash your hands with antibacterial soap when you are done working with tank filters or cleaning gravel.