Analogies should generally not be used to prove or disprove an argument. Rarely do two scenarios correspond perfectly, so it is unconvincing to say that because they are similar that a principle in scenario A definitely applies to scenario B.
If you are tempted to use an analogy it should be done in two parts: First explain scenario A and teach the principle that you believe connects the two scenarios. After explaining the principle you need to demonstrate how and why that principle applies to scenario B. It's this second step that is often skipped. When comparing disparate scenarios it is your responsibility to explain why that can be done.
You may need to do some of the work for you opponent when helping them understand that their analogy is weak or doesn't apply. Ask them to clearly state the principle they are demonstrating with the analogy and to explain why they think that principle applies to the original scenario.