By default ticket creators can close their own tickets, but this can be disabled so that people can't close their own tickets. This is so you have complete control over the ticket, or stopping people from spam creating of them.
To disable this, go to the panel (https://panel.parent.gg/)
Select your server and click "Modify" and find "Commands"
Once you have clicked "Commands" click "Close Command" and open up "Command Values" and mark it as Disabled.
All done, ticket creators can't close their command. If you're going to test this, if you have a staff role this will overrule this setting, so we would recommend you test this on someone who hasn't got staff permissions.