Exactly. If you can not do things separately in a relationship without one feeling excluded, that is not mature love. In mature love, both parties know and understand that each is an individual and must be able to have a life outside of the relationship. You do NOT always have to be together to be in a relationship.
Jealousy in a relationship is a fear of losing that person. It's insecurity. The relationship has not been nurtured to where both parties feel secure. A perfectly natural reaction when the relationship is important to the individual.