My girlfriend said, "You act like a detective too much. I want to split up."

My girlfriend said, "You act like a detective too much. I want to split up."
"Good idea," I replied. "We can cover more ground that way."

This joke is centered around a misunderstanding, and also an unfortunate event. It is also a bit absurd. The phrase "I want to split up" means that the two people should separate, however, the humor lies in the fact that the girlfriend likely meant "I no longer want to date you", and the jokester took the comment to mean that they should separate temporarily in order to pursue someone or some clue.

The fact that the girlfriend is breaking up with the jokester is also a bit funny since it is someone else's misfortune.

Finally, It is a bit absurd that the jokester wouldn't be able to recognize their own girlfriend's body language, and was unable to see this conversation for what it really is. Is anyone that dense?