Even when they're older, their natural instinct is to run and play. As an actively engaged parent, you want to join in that soccer game, jump rope with them, or go for a bike ride, right? Maybe you're keen to simply keep up with them, or lead by example, in terms of living a happy, healthy and active life?
Secondly, by starting out soft and slow, you're more likely going to establish strong and long lasting habits! Introducing new activities over time will allow you to mindfully integrate them into your normal weekly routine, rather than becoming overwhelmed by a mountain of new 'added extras' that need to be fitted in, or 'bolted on' to your existing commitments.