The problem is that to keep the books balanced, an ever greater inflow of foreign capital is needed to finance that deficit. Attracting that capital could be a problem is the deficit keeps getting bigger and bigger. Of course, not everyone agrees with his interpretation, as you suggest. A couple of months ago it seemd the fed had good cause to want to keep raising rates. But the markets appear to be correcting themselves.
Inflation is far from being out of control and unemployment is still low.
What possibly could Greenspan be worried about. My previous answer covers a lot of what he is worried about. But they also know that every recession in the past 50 years was preceeded by an acceleration of inflation and they want to slow growth enough to keep that acceleration from occuring. With rates rising and the Treasury buying back debt are there any real advantages for the bond market in all of this. I guess you could say there is an advantage for bonds if the Fed is successful in keeping inflation under control since long-term rates are highly sensitive to actual and expected inflation.