Some people have rings that are so tightly stuck that even soap does not help, but dental floss works for them. Meanwhile, others find dental floss painful even with a mildly stuck ring, yet soap works well for very tight rings. Why is some skin more sensitive to dental floss? And what makes some people’s skin respond better to either soap or dental floss?
Soap is decreasing friction. The dental floss done correctly should apply compression to the tissue and force fluid out of the area. This is especially helpful if a lot of tugging has resulted in swelling.
Okay, why does soap work better for some people, and dental floss works better for other people?
There is a difference because you have anecdotes, not data. You can’t draw conclusions from them. The entire “experiment” could be poisoned by a single person with joint disease. It could be poisoned by a single person lying about the severity of the pain etc.