This idea of ownership leads to attachments, not just in romantic relationships but across all aspects of life. The more we cling to the idea of 'mine', the more anxieties and jealousies we breed. We try to control elements of our lives that are, in truth, beyond our control. This is how attachment can lead to anxiety.
Do you have anxiety in your life. Maybe you are trying to place attachment and ownership on something that can't be attached to or owned?