why does a dc analysis is needed when working on a CE- Amplifier?

 

Because if the transistor's DC conditions causes it to be cutoff or saturated then it won't work.

 

why does a dc analysis is needed when working on a CE- Amplifier?

Think of a BJT as two opposing diodes. In order for it to work like a CE amplifier the collector to base junction needs to be reverse biased and the base to emitter junction forward biased. After these biases are established we can do AC analysis, but the AC voltage is still constrained by the DC voltage requirements mentioned above.