Why does he tell everyone I’m his girlfriend in front of me except me?

He likes to show me off in both of his jobs. The other day he told one of his bosses that he couldn’t go to work because he was w/ his girlfriend. (Not as an excuse because he works a lot and he was willing to go)
He wants to take a picture w/ me. During sex he spends the night and hugs me like I’m a prisoner. In the beginning he told me not to fall in love but his the one showing me off. 🤷🏽‍♀️
Why does he tell everyone I’m his girlfriend in front of me except me?
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