X-ray observations and non-detections of cool giants suggested a picture of a division

of warm solar-like giants with Coronae and cool inactive giants with cool winds instead,

first suggested by Linsky and Haish 1979. But in the meantime, photospheric magnetic field

has been detected in cool giants, and their chromospheric emission mostly surpasses the

"basal" flux, which is a minimum emission found in entirely inactive stars. Hence, the absence

of coronae in cool giants is not caused by a lack of magnetic activity! The real reason lies in

fundamental chromospheric physics, as we will show. Mayor evidence is provided by the 

Wilson Bappu effect: with lower gravity, density scale-heights increase. At the same time, 

chromospheric heating decreases and the "Athay point", at which the solar corona begins,

because chromospheric radiative cooling collapses by reaching full Hydrogen ionization, 

is not passed in giant chromospheres. A few case studies of eclipsing binaries with cool 

giants, providing a direct account of their chromospheric extent and density profiles, 

are presented to illustrate this explanation.