The jeweler probably doesn't like Tungsten because it is not as expensive as their platinum bands
I have a titanium and a tungsten band. What I heard when I was shopping is that they are so strong that if you have an accident and break your finger or it swells up then the hospital has to have a special tool or a laser to cut the band off, and you may be out of luck. However, Snopes says that is false, so I think you are good to go: snopes.com: Titanium Wedding Rings