You don't understand, my man (woman?).
The pope isn't the head of Christianity. There IS Christianity out there that he is not head of. Therefore, he is not the head of Christianity.
There is no piece of America out there that Bush is not the President of. He's the president of all of it.
Your analogy doesn't hold.
Sure it holds. The President has control over a certain geographical territory and people born in that territory. Now, some people recognize his authority over that territory and those people, others don't. Some people obey laws that he brings into existence concerning that territory and those people, others don't. Some people think he's a legitimate president, others don't. But personal opinion, the ability to be caught and brought before a judge, the willingness to prosecute people who are treasonous towards the President, these things don't change the facts. Bush is President.
Just change the word Pope for President and you've got nearly the same thing, except the Pope has authority over all the baptized. Whether the baptized choose to recognize that, whether anyone requires them to make that recognition - none of that is relevant to the facts.
Thanks for pinging me to this but I find these becomes circular arguments.
1) The Pope is the head of the Church;
2) The Church is Christianity;
3) Therefore the Pope is head of all Christians.
While this is flawed reasoning (premise 2 is only partially correct) you'll never get the Catholics to admit it. After all, this is what the Vatican says.