Couple of major things I see which are going to leads to major defects down the road.
NEVER ever use the same washing implement on the wheels as you do the paint. Even if the wheels aren't very dirty, you're still going to transfer brake dust and other fine metal particles into the washing implement and never get them fully out. So next time you use it on the paint it will leave defects.
When washing panels start from the top and work your way down. The dirtiest parts are the car are always going to be from the bottom. If you start at the bottom and go up you're going to bring that dirt with you and rub it into the paint.
NEVER USE A SQEEGE. Your partner was absolutely right saying not to trust that sound. The reason you use a microfiber towel and drying aid is to pick up any contaminants you left during the wash process. The squeegee is just dragging anything you left over into the paint.
Pro tip from one of the best detailers out there: don't use the two bucket method. Instead, use a microfiber towel for EACH panel. Microfiber towels are cheap and easy to clean. Relevant video at time stamp.
By using one microfiber towel per panel (or folding the towel on each new panel), you all but eliminate the possibility of transferring contaminants to a new panel.