Expand `ifthenelse` immediately

you can't use \ifthenelse inside \setcounter. Change the order:

\documentclass{report}
\usepackage{ifthen}
\newcommand{\thesissize}{SHORT}
\begin{document}
   \ifthenelse{\equal{\thesissize}{SHORT}}
    {\setcounter{page}{3}}{\setcounter{page}{2}}


  hey
\end{document}

Expandable tests are possible with expl3 and etoolbox. For both you should store the reference text in a command:

\documentclass{report}
\usepackage{expl3,etoolbox}
\newcommand{\thesissize}{SHORT}
\newcommand{\shortsize}{SHORT}

\begin{document}
\ExplSyntaxOn
\setcounter{page}{\tl_if_eq:NNTF\thesissize\shortsize{3}{2}}
\ExplSyntaxOff

\setcounter{page}{\ifdefequal{\thesissize}{\shortsize}{3}{2}}

  hey
\end{document}

Another version of a string comparison using the pdfTeX macro \pdfstrcmp. The following uses the pdftexcmds package to make it available to all engines under the same name:

\documentclass[]{article}

\usepackage{pdftexcmds}
\makeatletter
\newcommand\ifstreq[2]
  {%
    \ifnum\pdf@strcmp{#1}{#2}=0
  }
\makeatother

\newcommand\thesissize{SHORT}

\begin{document}
\setcounter{page}{\ifstreq{\thesissize}{SHORT}3\else2\fi}
hey
\end{document}

If a LaTeX syntax is preferred one can use

\documentclass[]{article}

\usepackage{pdftexcmds}
\makeatletter
\newcommand\ifstreq[2]
  {%
    \ifnum\pdf@strcmp{#1}{#2}=0
      \expandafter\@secondofthree
    \fi
    \@secondoftwo
  }
\providecommand\@secondofthree[3]{#2}
\makeatother

\newcommand\thesissize{SHORT}

\begin{document}
\setcounter{page}{\ifstreq{\thesissize}{SHORT}{3}{2}}
hey
\end{document}