Do I need to explain my reasoning when choosing between two offers

No. You do not need to explain your decision.

Assuming it's actually true, it would be appropriate to tell the department you're turning down that their offer was attractive, and that it was a difficult decision, and that the choice came down to non-academic factors that were out of their control. But even this is more than you need to tell them.

You don't need to tell them, but it is a nice thing to do: Since your decision came down to non-academic considerations, it would be a nice gesture to thank them for the offer and explain that you preferred the other university for reasons that are not within their control. Just as job applicants like to get useful feedback on an unsuccessful application, and a guy who gets turned down for a date wants to know why (is it something wrong with me?!), employers generally benefit from knowing why they were unable to recruit the candidate they wanted. I would leave out the bit about the 'gut feeling', but it is worth mentioning the other factors that led to your decision.