The White House has picked the first female general to head the Air Force in the Pacific, which will make her the first non-pilot to command air power in such a large theater of operation.
Is this correct?
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I'm assuming you want to limit this to US armed forces, since I'm not sure that gathering the data from every air force in the world is very feasible.
If that's the case, it certainly appears that way. Pacific Air Command (PACAF) has long been the largest area of responsibility in the US Air Force, covering over 100M sq miles, or just over half the world's surface area.
The name of the command has been changed over time (since the Army Air Forces era), but a relatively straightforward list of the commanders of this area is:
General George C. Kenney, 3 Aug 1944 Lt Gen Ennis C. Whitehead, 30 Dec 1945 Lt Gen George E. Stratemeyer, 26 Apr 1949 Lt Gen Earle E. Partridge (acting), 21 May 1951 General Otto P. Weyland, 10 Jun 1951 Gen Earle E. Partridge, 26 Mar 1954 Gen Laurence C. Kuter, 1 Jun 1955 Gen Emmett O'Donnell Jr., 1 Aug 1959 Gen Jacob E. Smart, 1 Aug 1963 Gen Hunter Harris Jr., 1 Aug 1964 Gen John D. Ryan, 1 Feb 1967 Gen Joseph J. Nazzaro, 1 Aug 1968 Gen Lucius D. Clay Jr., 1 Aug 1971 Gen John W. Vogt, 1 Oct 1973 Gen Louis L. Wilson Jr., 1 Jul 1974 Lt Gen James A. Hill, 1 Jun 1977 Lt Gen James D. Hughes, 15 Jun 1978 Lt Gen Arnold W. Braswell, 1 Jul 1981 Gen Jerome F. O'Malley, 8 Oct 1983 Gen Robert W. Bazley, 1 Nov 1984 Gen Jack I. Gregory, 16 Dec 1986 Gen Merrill A. McPeak, 22 Jul 1988 Lt Gen James B. Davis, 5 Nov 1990 Gen Jimmie V. Adams, 19 Feb 1991 Gen Robert L. Rutherford, 26 Jan 1993 Gen John G. Lorber, 12 Oct 1994 Gen Richard B. Myers, 7 Jul 1997 Gen Patrick K. Gamble, 23 Jul 1998 Lt Gen Lansford E. Trapp (acting), 9 Apr 2001 Gen William J. Begert, 4 May 2001 Gen Paul V. Hester, 2 Jul 2004-
There have been three commanders since that page's last entry, easily verifiable by Google:
Gen Carrol H. Chandler, Nov 2007 Gen Gary North, Aug 2009 Gen Herbert Carlisle, Aug 2012-
A quick perusal of their Wikipedia entries shows them all as pilots at one point in their career. I don't really see why those would be inaccurate, but you can follow them all to their primary sources if interested.