I didn't come up with this: it was a thing floating around Chinese social media a while back. I was reminded of it when I saw a similar exercise by Shaun Micallef.
At the time this joke was devised, the President of the People's Republic of China was Hu Jintao, but was expected to be replaced soon by Xi Jinping. The Premier at the time was Wen Jiabao.

1: Xi met with Obama.
2: Who?
1: No, Xi was at the White House.
2: Who?
1: Hu is the current leader of China. Xi met with President Obama.
2: The leader of China is a woman?
1: No, he’s not.
2: Who?
1: Right.
2: So the leader of China is a man, and he met with President Obama in the White House.
1: No, Xi met with the President.
2: I thought you said he was a man.
1: Who?
2: The President of China.
1: The President of China is a man, but Xi met with the President.
2: Why are you calling him ‘she’?
1: Because that’s his name.
2: Okay, let me get this straight. Someone from China met with President Obama.
1: Correct.
2: When?
1: No, Wen is the Premier.
2: Whose premier?
1: Yes.
2: Wait, whose premier is when?
1: Yes, Wen is his Premier.
2: I thought we were talking about a she.
1: Well, when Xi becomes President, the Premier will still be Wen.
2: When who does what?
1: When Hu steps down.
2: This is total insanity!*
1: No, Lin’s got nothing to do with this. He’s a basketball player on the New York Knicks.

1‘Linsanity’ is the name of the global following of NBA basketball player Jeremy Lin.