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.
\hfill? – tommy.carstensen Jan 10 '18 at 13:38