Why is my federal fee $120 and my state fee $60?

You appear to be using Live Deluxe Edition, which is a paid version--$120 for Federal and $55 for state (if applicable), and if you choose to pay the fees out of your Federal refund, there is an additional $40 service fee ($45 for California filers.)     Regular Deluxe without that Live feature is $60 for Federal and $50 for State.

The Live feature allows you to contact a tax expert CPA/EA on demand for help during return preparation, and a final review of your return by an expert before filing.

What product did you you think you were using or want to use?   Did you not want that Live feature?  It can be removed prior to paying and filing.

FAQ:  What is TurboTax Live?

https://ttlc.intuit.com/community/choosing-a-product/help/what-is-turbotax-live/01/27191

FAQ:  How do I remove Live?

https://ttlc.intuit.com/community/downgrading/help/how-do-i-remove-turbotax-live/01/27312