This can have a few meanings.
1.) He threatened to leave her if she continued to hang out with male friends.
2.) The man or woman interested in you may feel threatened when they notice they have no chance at dating you or getting close to you as they realize you have your eyes on somebody else and it not be them. They will show lack of interest in you at that moment and begin to ignore the two of you with a defense mechanism to protect themselves and avoid conflict at any and all cost.
1.) Her parents warned her that her decision to disobey meant all privleges would be taken away. She felt threatened and decided to obey.
2.) If person (#1) likes you a lot and has interest but you do not like them in that fashion the rejection can make them feel threatened especially if there is a person (#2) that you are seeing.