Why is my shell script giving the same output for every case?

Brackets do not work like parenthesis in test expressions. Also, test uses =, not ==. And you also need to split to expressions properly into tokens (by adding spaces around the = signs). So what you want, rather, is this:

if [ "$CHAR" = Y -o "$CHAR" = y ]; then    echo "YES"elif [ "$CHAR" = N -o "$CHAR" = n ]; then    echo "NO"fi

Notice that I've also quoted "$CHAR". This makes the program more robust in the cases where $CHAR is empty or contains spaces. The Y and N, on the other hand, do not need any quoting as they are constants and contain no whitespace.

To be more precise, what happens in your program as that each of the $CHAR expressions expand to a single token that looks something like [N==Y], which is a token without special significance for test. Any token that lacks special significance is interpreted by test as a "true".

You need to use single = for string comparison and you've too many brackets. So the code becomes:

#!/bin/bashread CHARif [ "$CHAR" = "Y" -o "$CHAR" = "y" ]; then  echo "YES"elif [ "$CHAR" = "N" -o "$CHAR"="n" ]; then  echo "NO"fi

Next time when you'd like to debug your script why it doesn't work, run is as: bash -x ./script.sh or add -x in your first line after bash.

Check the following one-liner:

read CHAR && [ "${CHAR^^}" = "Y" ] && echo YES || echo NO

It's using bash parameter expansion, see: Case Insensitive comparision of strings in Shell script.

a case statement can be quite readable

read charcase ${char,} in  y*) echo Yes;;  n*) echo No;;esac

https://www.gnu.org/software/bash/manual/bashref.html#Shell-Parameter-Expansion