Why does radar processing always require FIR filters?
Radar often uses phase as part of the signal. After down converting you are going to have a signal that is normally "relatively" low frequency(kHz compared to GHz).

When designing a Digital filter you can get very good brick wall filters. The major difference is that FIR filters can be symmetric and have linear phase delay. Linear phase delay means a flat group delay which correlates to the phases being preserved. 

When phase is a major part of your signal(in CWFM radar it makes up the position part of the signal) any phase delay can cause a incorrect reading.