what does it mean when your partner doesn't want to show you off?

Interest Deficit
One particularly unpleasant reason a partner may have checked out is that they have lost interest in the relationship and no longer want to continue it.
Distraction
It's possible that your S.O. is under the stress of having other things on their mind, such as an excruciatingly difficult work project or personal and/or familial issues that sap their energy.
Embarrassment
Your behaviour is poisonous and negative if every word out of your mouth is an insult, a critique, or a derogatory remark, and no one wants to hear it, least of all your S.O.