PelleS
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Yes, the figure 2.55 circuit is used to demonstrate the problem, figure 2.57 is solving it.Your transistors need some BIAS. That is a small voltage (~ .8V) to turn on (open up) the base emitter junction. The top transistor needs its base at 1/2 Vcc(V2) + .8V, the lower needs 1/2 Vcc(V1) -.8V.
R2 in your circuit is usually the collector of an NPN transistor so it can swing the base of the PNP output transistor completely to ground.