The quoted text from the book is:
In the quiescent condition, \$V_o = 0\$ and \$V_1 = 0\$ .
This is correct in the sense that these are the conditions under which no current flows through the stage, and the output is at 0V.
This appears to be from you:
What forces \$V_1\$ and \$V_o\$ to be equal \$0\$ when \$V_i = 0\$?
The answer is nothing. The question's premise isn't true. The "quiescent condition", as described, requires \$V_i\$ to have some specific value which is neither 0 from ground, nor from \$-V_\text{CC}\$. It is that value which turns on \$Q_3\$ just enough so that exactly the right amount of current flows through \$R_1\$ to create the correct voltage drop for the conditions.
That value would arise, in the overall amplifier, thanks to feedback. When the overall amplifier (not shown) is configured with a feedback network, say for unity gain, an output of 0V would be ensured by tying the input to 0V. Internally, the right condition will arise in the \$Q_3\$ circuit.
But it will not be the case that \$V_i\$ is zero from any obvious reference point. The voltage will be somewhere in the neighborhood of \$Q_3\$'s \$V_\text{BE}\$ (above \$-V_\text{CC}\$), since that transistor has to be partially turned on and be in its active region: neither saturated, nor cut off.