Disadvantages

Blockage of primary aperture by secondary
Produces near sidelobes and loss of efficiency
Large field of view requires large secondary making efficiency loss worse

Secondary support structure scatters light
Far sidelobes
Further loss of efficiency

Secondary illuminates annulus between receiver entrance aperture and edge of primary hole
More far sidelobes (although can baffle)

Diffraction from edge of secondary
More far sidelobes