How to left align the cases in Latex?

Try in-line math instead. Note: this will not number your cases.

\documentclass{article}
\usepackage{enumerate}
\usepackage{amsmath}
\begin{document}
\begin{enumerate}[(i)]
\item Statement 1.
\item $X_r = \begin{cases}
 2r-2, & \text{for $k = 1$,}\\
 2r-3, & \text{otherwise}.
\end{cases}$        
\end{enumerate}
\end{document}

Another alternative for JouleV solution would be to use flalign from amsmath as in

\documentclass{article}
\usepackage{enumerate}
\usepackage{amsmath}
\begin{document}
\begin{enumerate}[(i)]
\item Statement 1.
\item \begin{flalign}X_r& = \begin{cases}
 2r-2, & \text{for $k = 1$,}\\
 2r-3, & \text{otherwise}.
\end{cases}&\end{flalign}
\end{enumerate}
\end{document}

to get: