When a relation is jealous because you got the supervisor role and he didn't and now refuses to listen to you as a supervisor and dosen't work as a team member now, could that be classed as insubordination?

As far as I understand , failure to follow or carry out instructions issued by a supervisor is insubordination

https://www.askmehelpdesk.com/workplace-relationships/supervisor-who-wants-advice-personal-grievances-485408.html

Is this the same person as in this thread?? Please define what the relation is to you, family, friend, or lover.

Insubordination is defined as "a willful failure to obey a supervisor or an employer's lawful orders".

If you are the one in the supervisory role and are respresenting the company, then it is your job to talk to the person and possibly give the person a warning that if the behavior continues that their job will be in jeopardy.