This is a good question.
The answer is, it depends what you are trying to do.
For example, if you (or your parent) is trying to register for a program or get an ID that requires proof of citizenship, then yes, you need a citizenship certificate.
However, otherwise you do not need to have a piece of identification on you that proves your citizenship. If somebody is telling you that you need to prove your Canadian citizenship even though you’re not trying to apply for anything, they are lying to you.