X demands or desires action , inaction or liability from Y and the grounds X uses is "if you were in my situation, you would want this too" or "what if this had happened with you" but then Y can flip this back and ask back the same question "What if YOU were in MY situation here , would you still make these demands ?"
At that point if one party fails to empathise with the other then everything falls apart. Is it even possible to truly understand opposing values or stakes even if your needs are more immediate
Assuming both parties do empathise with each other's opposing values and stakes , how would one come to conclusions about what stakes or interests or goals matter more ? And who's goals to prioritise ? And what compromises should be made and why.
Because even if people did empathise with each other's opposing positions doesn't mean they'd neccessarily value their own position any less
An example would really help
Basically
Freedom of speech yay
Response: "what if someone said X to you or your loved one , would you tolerate it ?"
It might be helpful to separate feelings from facts and ideas.
"While i would be upset if someone said X to me, it would not change my position that freedom of speech is desirable in society."
This is specific to your example but can apply in other situations where you can empathize with someone but still defend a position that is seemingly opposed to those person's feelings.
If I'm one of the parties in this I'll start by not attempting a reversal but instead an acknowledgement.
Regardless of my thoughts on the matter they truly feel the way they do. That's not up for debate, so acknowledging their feelings would be step one for me
I would try and hear their view with receptivity and see what resonates with me. Then I'd say "It makes sense that you feel x about y, I would have a difficult time with that too"
Then you have the chance to have a conversation instead of a debate