There are lots of reasons not to eat fish. There are a lot of people who don't consider fish to be in the same category as other animals. I guess it is because fish are not cute and cuddly. They don't have fur, they don't show emotion, and the seem to be de-void of personality. Also, we tend to think of fish as "disposable" pets. If they die we flush them and forget them. Hence, people seem to think that they can eat fish and still justifiably call themselves vegetarians.
If you eat fish you are not a vegetarian. You are however taking a step in the right direction. Fish are full of contaminants. This is why pregnant women are advised to steer clear of them. Fish live in waters which, have now, been polluted by man. Anything that gets dumped in the water is inside the flesh of the fish you are eating.
Fish that are farmed are kept in horribly cramped and dirty conditions. They swim in their own filth and bump into each other, causing horrible injuries.
When they are harvested fish are basically suffocated to death. A cruel and painful way to die. The world's oceans are becoming barren wastelands because of overfishing. If you have taken the step to cut out mammals from your diet take the next one and banish fish as well.