Our last hint for convincing nay-sayers that fishing is fun is to simply take them with you. Sometimes, they must see for themselves.
Now, before you do that, it's worth it to evaluate the person you are trying to convince about the hobby. Is this someone who hates the idea of sitting on a blistering dock threading worms onto a hook for bluegill? Maybe you'll want to skip that as an intro to fishing and instead focus on using a kayak and artificial lures that can be worked fast. That way it keeps their attention.
Or maybe the person is a health nut. You need to find a way to introduce it to them in a way that highlights the benefits I already talked about in this article. Really hammer home how much more satisfying a hand-caught fish meal is to one pulled out of the frozen food section at Wal-Mart.
Maybe the person thinks fishing is boring. That's easy, take them out fishing for a big, aggressive predatory species like barracuda or northern pike. Perhaps the person is a nature nut who doesn't understand how fishing will enhance their love of the outdoors. In that case, find a nice, secluded and peaceful place where they stand a good chance of seeing a moose on the shore or an eagle flying above. It may not take them long to come around.
Simply put, if you're trying to convince someone fishing is awesome by showing, you need to cater the experience to them and their likes and dislikes. If you do it properly, we're betting it will only take a few hours for them to finally come around on angling!