why wont Bose sounddock xt play music on my iphone 7

you would need to ask Bose if this product is supported with your new device. It's their product, and their decision to continue support or not

http://worldwide.bose.com/productsupport/en_us/web/sounddock_xt/page.html#tab=co ntact_tab

Hi I have the exact same problem since recent update to iOS 10.2.1. iPhone 5s. My Sounddock XT is brand new (January). Tried on the dock several IPhones (5s and 6) with 10.2.1 : charges only. Tried through the AUX the music flows through and the volume works fine. My daughter's IPhone 5s still on IOS 10.1 works perfectly fine. Culprit is therefore the iOS upgrade. Is apple going to correct this rapidly or should I bring back to Bose the SoundDock (150$ is not negligible) ?

Even if the issue lies with iOS (and there is really no certainty that it is), contacting Bose support as previously suggested would still be your best bet. Could be as simple as a need to update the dock's firmware or a setting on the phone. Bose would be in a better position to assist with that.

Thanks. Just hung up with them - after a dozen of over-the-phone checks and tests confirming the issue, Bose is going to take the sounddock back and swap for another which -hopefully- should be working for the whole family. Great day to you.