A parent should provide their kids with opportunities to try new things. Sometimes this might require gently making a kid do something at least a few times until it's clear it's not something they are good at or interested in. Also deciding when to try something is important - kids might need to try it at different ages. And of course convincing and reassuring a kid might be necessary to try something they are afraid to do. Until the age of 12 or so, it's important to make it fun, at least initially.

It's debatable whether a parent always needs to "lead by example": for example, I've never played hockey, but I introduced my son to it, and he played for a while (until injuries made us reconsider and he stopped). For mental well-being, make sure to not display your worst emotions in front of your kids - they will definitely notice, and will probably carry it for the rest of their lives.