So what? Italy is the ancestral homeland of the American mafia, but Italians are hardly responsible for gangland murders and thievery in the US. America is the homeland of the Ku Klux Klan, but Americans as a whole did not endorse the KKK. The Yemeni people have not made war on America.
“AQAP” (for Al Qaeda in the Arabian Peninsula) is a reified category composed of an article in Arabic (al), an Arabic proper noun (Qa’ida), and a compound proper noun in English (Arabian Peninsula). It has no literal meaning in either language. Essentially a guerrilla group made up of a few hundred really bad actors, the AQAP is hardly the “threat to the American homeland” of the old USSR, although the quadrilateral acronym seems to elevate it to that status.