When you learn to trust, you stop being possessive. But a true gf/bf will know how to never put you in a situation where you become possessive. I tell my gf (when I had one) each and every bit of what happened so she never had to be doubtful or curious.
Its a known human behaviour for persons to keep different levels of relationships going as a form of 'insurance". If the relationship dissolves then those less intense ones are "Plan B' to survive as social creatures.
Do you have someone you would go for if dumped ? Maybe relax and accept our human nature.
If you possess something (bird in a cage) you can never know if it truly wants to be with you.
If you set something free and it returns you know it truly wants to be with you.
Sometimes talking to a professional will help you realize why you are that way to begin with. Usually it's because of something you grew up around or an earlier relationship that has marked you indefinitely.