Some conversations become impossible because both people are trying to win different games.

Two people can be having entirely different conversations without noticing. One is trying to solve a problem, the other is trying to be understood. One wants a decision, the other wants an acknowledgement. Both feel unheard, and neither is being unreasonable.

When a conversation is going nowhere, stop and ask what each of you is trying to get from it. Sometimes just naming it resolves the whole thing. Do you want help with this or do you want me to listen is a plain question, and it prevents a great many pointless disagreements.