As a fishing coach, I've always said that we can enllighten 99.9% of people of the value or enjoyment that fishing brings, and most will be happy that the fish are not harmed (coarse fishing anyway). I've 'converted' dozens of vegetarians to fishing, but in my experience, 'ethical vegans' (more vegan than dietry vegans) present an altogether different challenge.
Trying to sell the virtues of coarse fishing to a hardened vegan is pretty much out of the question, especially if using livebait like maggots.
I did however have some success on a fly-fishing beginners day teaching a young vegan woman. She enjoyed tying the flies, and learning casting-techniques. She even had a go at fishing, provided that we tied a piece of red wool onto her line, instead of a fly based on a hook.
The downfall came when the hungry rainbows in the well-stocked pool started to show themselves and "take" her wool lure. She asked why there was so many fish, and we told her that they were farm-bred fish that had been stocked only the day before, at which point she put down the rod and marched back to the car park.
piscator non solum piscatur