Keeping things to yourself does not mean keeping them a secret. Assertiveness comes from confidence, while secrets come from fear. Sharing is expressing yourself confidently without reservation and without any pressure to convince others or justify your own thoughts and beliefs.
Here is a list of things you can keep to yourself or share selectively. If you are confident about them, you do not need validation, approval or to have the majority with you to hold them. If you want someone’s opinion, ask. If someone asks for your opinion, respect their choice not to accept it or to do whatever they want with it. If they disagree, do not like it or do not want to use it, it should not create any doubt in you. Some things are yours to keep and you can share them, but never with pressure. Pressure is not assertiveness.