Typically to "grow up" is used when talking about getting older. For example, a child might say, "When I grow up, I want to be a doctor!" or if you haven't seen your neice/nephew in a few years and they're mature you would said, "Wow, you've really grown up!". Also sometimes children will refer to adults as "grown ups". Or you might tell someone to "grow up" when they're being immature.
To become a better person (in this case by trying to make decisions for reasons beyond their likes and dislikes) would be "to grow".
1. If you always choose what you like, you are actually rejecting a myriad possibilities in life. You should give a try to what you don't like, try to get out of your comfort zone and grow. Part of growing is being able to make choices for reasons beyond likes and dislikes.
2. Always making choices based on our likes and dislikes costs us infinite possibilities in life. Give a shot to things you don't like. Step out of your comfort zone and stop making decisions based solely on your likes and dislikes. That is what help you grow.
Also in #1 you started by talking about "we" and then switched to "you", and you would want to make it all one or the other. In this case I switched it all to "you".