The issue is that break is not a keyword in Perl. You mean last. For a basic intro to how to control programmatic flow in Perl, see Loop Control in perlsyn.

If you had used strict, Perl would have told you as much.

use strict;
use warnings;

while (<STDIN>)  {
        print "--> $_";
        if ( /^2/ )  {
        break;
        }
        print "--> $_";
}

while (<STDIN>)  {
        print "==> $_";
}
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yields

Bareword "break" not allowed while "strict subs" in use at fluff.pl li
+ne 7.
Execution of fluff.pl aborted due to compilation errors.
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Please read Use strict warnings and diagnostics or die (and The strictures, according to Seuss for a chuckle) to understand why strict will make your life dramatically easier.