I went in to franchise management to delete my team but the buttons were grayed out. How do I delete my team, or can I only do it between seasons?

This is the first I heard about the Team Management page or the edit/delete functions at all. Learned something new about FC Dynasty after about 10 years of playing it haha.

Can I ask why you're leaving the game?

Something new, me too. Never looked at that page before.

AFAIK FC Dynasty allows only one team per user name. If you have an alias, use it to start another team. To be removed from a team you have to not check in on it for... I forget how long... and eventually the team will revert to AI. At which point I assume you'd be free to start another team under this name.