I agree with the contractor. At least in my area they are required to be vented through the roof. Might want to check with the local code enforcement folks.

You can also transition from 4" round to oval, and then back to round where it connects to the outside cap. The oval shape easily fits inside a wall and you can maintain the same cross-sectional area. Even Amazon carries a variety of oval duct and fittings. Below is one example that is used for a dryer, but you could use it with a fan as well. Or you could just get fittings and make up your own to fit your situation. Here is a link that might be useful: Round-to-oval-to-round periscope duct

If the soffit is that narrow I don't think you'll be able to access the angle of the rafters in order to install a vent, an elbow, and the duct pipe. I'm assuming this soffit is vented? If so, any moisture that exits your exhaust pipe will be drawn back into the attic along with the fresh air the vents pull in. As the link below explains, the best solution for you will probably be to install the vent thru the roof. Here is a link that might be useful: venting

ok, thank you for that input. I will leave that vent alone, other than replacing the ugly bent looking grille. I thought it would have been an option rather than cutting a new hole. The other bathroom on the main floor vents out a side wall (northside of house) And i have never had any problems with it. The fan is installed on the ceiling about 4-5 feet away from the wall. Not sure what kind of treatment they did with that as it is original to the house. lol - that upper area on my side of house looks like a good spot. how about if i run pipe (not a flexible one) and insulate the pipe to a different spot and do same? (still kinda stuck there) what if i did solid pipe to the vent and insulated it? and far enough away from attic vent so nothing flows back in that way? I've also seen vents that go on outside wall, and also ductless vents (did not look like a good choice).