Why should we charge the capacitor halfway in 555 timer circuit(as given in datasheet)?
The equations can be calculated. In the datasheet based on figure 14 it shows the well known astable mode of operation. In this operation the capacitor charges up to \$\dfrac{2\,V_{cc}}{3}\$ through \$R_A\$ and \$R_B\$ and later discharge through \$R_B\$ until \$\dfrac{V_{cc}}{3}\$, which leads to:
\begin{equation}
\dfrac{2\,V_{cc}}{3} =V_{cc}+ (\dfrac{V_{cc}}{3} - V_{cc})e^{\frac{-t}{(R_A + R_B)\,C}}
\end{equation}

Solving for t we have:
\begin{equation}
t=ln2\,(R_A+R_B)\,C = 0.693\,(R_A+R_B)\,C
\end{equation}