Malala Yousafzai was shot by Taliban hitmen in response to her activism and constantly speaking out against the Taliban. When she got to a Pakistani hospital, the doctor informed the government that they could not take care of her in Pakistan.
The government suggested England however they could not formally request that England take her because that would mean admitting that they could not take care of their own. They also did not want the Americans involved due to the recent Bin Laden raid that was done without the Pakistanis being informed.
In the end the United Arab Emirates offered to help which was more acceptable because they are a Muslim country.