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The code $\LEFTRIGHT\{\}{S_n}$ produces
whereras the code $\left\{ S_n \right\}$ produces
.
Is this a bug or feature? As the content in the braces grow larger, the visual effect of the unbalance is reduced. The above output of \LEFTRIGHT really looks ugly to my eyes.
Note: my preamble has \usepackage[lite,subscriptcorrection,nofontinfo]{mtpro2}
The answer is in the definition of \LEFTRIGHT, which means it is so “by design”:
\def\LEFTRIGHT#1#2#3{%
\specdelim@#1%
\ifspecdelim@
\LEFTRIGHT@#1.{\vc@nt@r{#3}}%
\else
\left#1
\vc@nt@r{#3}%
\right.%
\fi
\kern-2\nulldelimiterspace\mskip-\thinmuskip
\specdelim@#2%
\ifspecdelim@
\LEFTRIGHT@.#2{\vphantom{\vc@nt@r{#3}}}%
\else
\left.%
\vphantom{\vc@nt@r{#3}}%
\right#2%
\fi}
For strange reasons, \mskip-\thinmuskip is added (it's the same as \!).
Indeed, if you try
\documentclass{article}
\usepackage[lite,subscriptcorrection,nofontinfo]{mtpro2}
\begin{document}
$\{S\}$
$\left\{S\right\}$
$\LEFTRIGHT\{\}{S\,}$
\end{document}
you get
\PARENS{S_N}and\LEFTRIGHT(){S_n}behave differently.$\left\{S_n\right\}$is wrong to begin with; so is\LEFTRIGHT, independently from the strange behavior. Use automatic sizing only when really necessary, which is not the case here.