I’m trying to setup my Apple Watch series 3 and it keeps unpairing?

The current shipping Apple Watch Series 3 and 5 models require an iPhone 6s, SE, 7 or newer running iOS 13.  It will Not pair with the iPhone 6 or older.

Do you by any chance have an iPhone 6 or older?

iPhone -> Settings -> General -> About -> Model Name

Apple Holiday Return Policy (Purchase between: 15-Nov-2019 thru 25-Dec-2019, Return by 8-Jan-2020)

All purchases made before November 15, 2019 and after December 25, 2019, are subject to the Standard 14-day Return Policy. 

https://www.apple.com/shop/help/returns_refund

How far through the following set-up,are you getting? Set up your Apple Watch - Apple Support

Which iPhone, and which iOS version?

Tried resetting the watch, and then re-pairing?