This is most analogous, because it involves an attempt to do something impossible. The people who reject objectivism regard the quest for objective truth as something impossible, because there’s no such thing as a neutral, objective observer.

This doesn’t involve an attempt to do something inherently impossible. Someone searching for a valuable mineral among worthless stones is searching in the wrong place, but it might still be possible to find a valuable mineral by searching in a different location. The people who reject objectivism wouldn’t think that it’s possible to find truth by searching in the right place.

This doesn’t involve an attempt to do something inherently impossible. This involves an attempt to do something time-consuming and difficult.

This doesn’t involve an attempt to do something inherently impossible. Although one might be making a bad comparison, since apples and oranges are so different, it’s still possible to compare an apple to an orange.

This doesn’t involve an attempt to do something inherently impossible. We have no reason to think it’s impossible to scientifically analyze a chemical compound.