Is there a logical fallacy to describe trivial criticism of an analogy?

Person A makes an analogy between two crimes.

Example:

"When a woman robbed this store, the court let her go. But, when a man robbed this store, he was sent to prison."

Person B responds by basically stating that the analogy is imperfect; Person B's response contains no real or relevant argument.

Example:

"Well, the man's crime was completely different. His crime occurred on a different day of the week."

While Person B is correct in that differences between the two different cases exist (obviously), Person B totally ignores the core of Person A's argument. By focusing on the difference of a meaningless detail, Person B looks like they have just invalidated Person A's analogy, when, in reality, Person B ignores the real analogy.

Is there some sort of term to describe Person B's fallacy? I notice that this exact splitting-irrelevant-hairs trick is used (deliberately or not) all the time in arguments.