Population about 190 million. In possession of Nuclear Weapons. After the bin Ladin/Abbottabad Operation on May 2, 2011 an angry Pakistan closed the U.S. Military Base at Shamsi. Should America care about one airbase 7,661 miles from Los Angeles? Why should America care about Pakistan at all?
One reason is Pakistan is a large country with a capable nuclear armed military. Why not care about Pakistan on that basis alone?
Pakistan is a religious country. Islam is the State religion. The population is 95% to 98% Muslim. Only Muslim’s can hold the highest political offices. Pakistan does not trust America. It detests Israel and India. But it tolerates America because America has some things Pakistan needs. Arms and money. And America has given both with American tax money taken from Americans with no requirement for Pakistan to pay back America. Pakistan believes it is entitled to be supported by American money according to Magnificent Delusions: Pakistan, the United States, and an Epic History of Misunderstanding by Husein Haqqani.
Pakistan and China are closer than Pakistan and America. China has been a reliable ally for Pakistan although the reliability of both Pakistan and China are problematic for America. But it is important to recognize reality which is Pakistan and America do not trust one another. President Reagan had good advice for that. Trust but verify.
The answer to the headline question is: Pakistan and America are very important to each other.