This is because there are many different types of vegetarians. Pesco-vegetarians choose to eat fish. It also depends on your region. For example, eating fish in France is considered to be vegetarian.
Lacto-vegetarianism includes dairy products but excludes eggs, ovo-vegetarianism includes eggs but not dairy, and lacto-ovo vegetarianism includes both eggs and dairy products. There is semi-vegetarianism too.
Semi-vegetarians see white meat (eg. chicken, fish, turkey) to be more "proper" in eating, rather than red meat (eg. beef, lamb, pork). It may also do with the specific person's beliefs, e.g. they might see the catching of fish to be more redeemable than the actions of slaughtering an animal.
It will all depend on the person, thier knowledge of their lifestyle choice, geographical location, and personal beliefs.