A white scarf air force is one that values aircraft above all else (space-, cyber-, missile-warfare, etc.), i.e. an air force that is unwilling to evolve beyond flying planes:
In this regard, the greatest challenge that the USAF must overcome is its inability to focus on the ends rather than on the means. When the USAF finally realizes that it greatest strength comes from its ability to take advantage of all elements within the airpower domain (air, space, and cyber, and not merely on a particular system, that is when the USAF will have obtained a level of maturity capable of sustaining its operations without fear of continual, periodic change. This long-view transition will require the USAF to force itself out of "white scarf syndrome," where the means (flying aircraft) are more important than the ends of providing the nation with the greatest possible amount of airpower options. Unfortunately, if the USAF continues to rationalize its existence under the pretense of decisive operations, continually strives to prove its independence, and views its primary mission in terms of the aircraft it flies, then its future validity and relevance is questionable.
— Smith, Jeffrey J. Tomorrow's Air Force: Tracing the Past, Shaping the Future. Indiana University Press, 2013. p. 221.
How that fits in the comment about the A-10, I'm not sure, but as @Gerry noted, "You don't get to be an Ace killing tanks or hauling troops."
The term refers to WWI pilots who wore white scarves. (Regulation outfit over at nationalmuseum.af.mil.)
The silk scarves were smooth so they did no chafe the skin when looking around, they kept the pilots warm in the open-cockpits, and were used in cleaning the oil and rain off the goggles—bright colors are good since you know which part is clean and thus can be used.