No, it’s not a legitimate reason for claiming the moving expense on your California return. The move must be related to your workplace when you’re either an employee or self-employed.
According to Who Can Deduct Moving Expenses -- Non-military Members in the 2021 Instructions for Form FTB 3913, Moving Expense Deduction:
If you move to a new home because of a new principal workplace, you may be able to deduct your moving expenses whether you are self-employed or an employee.
[Bolding mine.]
See also What About Moving Expense Deductions? in New To California for more information.
