You are using \includegraphics[width=12cm]{FIGURE2}
where as your 0.5 text width
may not be 12cm. You should be using width=\linewidth
You can use width=\textwidth
also as subfigure
is actually a minipage
and \textwidth
refers to the width of text inside minipage
. And don't leave a blank line in between subfigures as it would indicate a paragraph break. With this, we have
\documentclass{article}
\usepackage{subcaption,graphicx}
\begin{document}
\begin{figure}[t]
\centering
\begin{subfigure}[t]{.5\textwidth}
\centering
\includegraphics[width=\linewidth]{example-image-a}
\caption{Really long text over 2 lines Really long text over 2 lines Really long text over 2 lines Really long text over 2 lines Really long text over 2 lines Really long text over 2 lines}
\label{fig:bestC1Sitting}
\end{subfigure}%
%%% Don't leave blank line
\begin{subfigure}[t]{.5\textwidth}
\centering
\includegraphics[width=\linewidth]{example-image-b}
\caption{Really long text over 2 lines Really long text over 2 lines Really long text over 2 lines Really long text over 2 lines Really long text over 2 lines Really long text over 2 lines}
\label{fig:bestC1Standing}
\end{subfigure}
\end{figure}
\end{document}

Looking UGLY isn't it?. We need some space in between. So change \begin{subfigure}[t]{.5\textwidth}
to \begin{subfigure}[t]{.45\textwidth}
with a \hfill
in between the subfigures.
\documentclass{article}
\usepackage{subcaption,graphicx}
\begin{document}
\begin{figure}[t]
\centering
\begin{subfigure}[t]{.45\textwidth}
\centering
\includegraphics[width=\linewidth]{example-image-a}
\caption{Really long text over 2 lines Really long text over 2 lines Really long text over 2 lines Really long text over 2 lines Really long text over 2 lines Really long text over 2 lines}
\label{fig:bestC1Sitting}
\end{subfigure}%
%% % Don't leave blank line
\hfill %% <--- here
\begin{subfigure}[t]{.45\textwidth}
\centering
\includegraphics[width=\linewidth]{example-image-b}
\caption{Really long text over 2 lines Really long text over 2 lines Really long text over 2 lines Really long text over 2 lines Really long text over 2 lines Really long text over 2 lines}
\label{fig:bestC1Standing}
\end{subfigure}
\end{figure}
\end{document}

I also don't get what's the point of \textwidth or linewidth? Are this relative positions?
\textwidth
is generally the global width of the text area. The parameter \linewidth
contains the line length inside a list (or derived) environment and it may change in a nested list (while \hsize
, \textwidth
and \columnwidth
don't change).
See egreg's answer from which I borrowed above lines. Hope it will be clear.