if I remove square brackets around $user, the program will just output every line refusing to perform grep function.

This is because you need to force the evaluation of the $user variable. This is an example under the Perl debugger of one possible way to do it:

  DB<1> @array = qw /foo foobar bar barfoo fobar foobaz /;

  DB<2> x  @array;
0  'foo'
1  'foobar'
2  'bar'
3  'barfoo'
4  'fobar'
5  'foobaz'
  DB<3> $user = "foo";

  DB<4> @a = grep /^\Q$user\E/, @array;

  DB<5> print "@a";
foo foobar foobaz
  DB<7> print join " ", grep !/^\Q$user\E/, @array;
bar barfoo fobar
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But using square brackets does not work as expected because it is defining a character class:

  DB<8> print join " ", grep !/^[$user]/, @array;
bar barfoo
  DB<9> print join " ", grep /^[$user]/, @array;
foo foobar fobar foobaz
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On the other hand, using ${user} instead of $user will be sufficient to get it to work properly:

  DB<27> print join " ", grep /^${user}/, @array;
foo foobar foobaz
  DB<28> print join " ", grep !/^${user}/, @array;
bar barfoo fobar
[download]