Go together and fit

[Rachel Adams]

Can I use either "go together" and "fit" in my sentence?

"He says he loves animals, but goes hunting every weekend. That does not really go together/fit."

 

[Yankee]

Can I use either "go together" and "fit" in my sentence?

"He says he loves animals, but he.goes hunting every weekend. That does not really go together/fit."

I would understand either one , but prefer "fit".