My three year old son is very clingy

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How do I encourage my son to be more independent without making him insecure? I want to give him a safe place to grow from, but he seems to really especially attached to me. I know it's not a bad thing that we have a close relationship unless it makes him wary of interacting with others. I had the same kind of relationship with my mother and I was painfully shy growing up. I don't want that liability for my son. Anyone have any suggestions?