We, like all living things, have to eat. Although I'm an 'almost vegetarian', I recognise that meat and fish are very important foodstuffs. My point is that animals that must be killed for food should be killed in as humane a way as possible (which is why I have criticised halal and kosher practices on other threads). Killing animals for entertainment (bullfighting and fox hunting, for example) is despicable.
Now to get off my high horse (no, I'm not a fox hunter) I suppose that fishing, whether for food or for sport, would be OK if fish, as has been suggested, feel no pain. If you google the subject, though, it appears that the jury is still out on that point.
Interestingly, Germany of all places has outlawed certain types of fishing.