#!/usr/bin/perl -w
use strict;
use warnings;

my $ins=0;

my @insert1 =  qw(1 1 1);
my @insert2 =  qw(2 2 2);

my $outfile = 'delme.txt';

open OUTFILE, '>', $outfile;
print OUTFILE <<DATA;
first second third
1 2 3
x y z
DATA
close OUTFILE;

insert (@insert1);
@ARGV = $outfile;
$/ = undef;
print <>;

insert (@insert2);
@ARGV = $outfile;
$/ = undef;
print <>;


sub insert{
  print "insert called:". $ins ."\n";
  $ins++;
  my @toBeInserted = @_;
  
  open(FILE2,$outfile)||die "you stupid fuck, file doesn't exit\n";;
  open(FILE3,">"."tmp.file")||die "you stupid fuck, file doesn't exit\
+n";;
  my $cnt=0;
  while (<FILE2>){
    chomp;
    my @fields = (split /[ \t]+/,$_);

    push(@fields,$toBeInserted[$cnt]);
    foreach(@fields){
      my $tmpString = $_ . "\t";
      print FILE3 $tmpString;
    }
    print FILE3 "\n";
    
    $cnt++;
  }
  
  close(FILE2);
  close(FILE3);
  #now swap the files
  unlink($outfile) || die "Cannont delete old file.\n";
  rename("tmp.file", $outfile) || die "Cannot rename file\n";
}
[download]

insert called:0
first   second  third   1
1       2       3       1
x       y       z       1
insert called:1
first   second  third   1
1       2       3       1
x       y       z       1
        2
[download]

Consider:

use strict;
use warnings;

my @insert1 =  qw(1 1 1);
my @insert2 =  qw(2 2 2);
my @inserts = (\@insert1, \@insert2);

my $outfile = 'delme.txt';
my $ins = 0;

open OUTFILE, '>', $outfile;
print OUTFILE <<DATA;
first second third
1 2 3
x y z
DATA
close OUTFILE;

for (@inserts) {
    insert (@$_);
    local @ARGV = $outfile;
    local $/ = undef;
    print <>;
}

...
[download]

Prints:

insert called:0
first    second    third    1    
1    2    3    1    
x    y    z    1    
insert called:1
first    second    third    1    2    
1    2    3    1    2    
x    y    z    1    2
[download]

Note that the bogus result from your reworking of my code was due to $/ being set to undef and therefore the <FILE2> seeing the entire file as one line on the second iteration. Sometimes I include "interesting" ways of doing stuff to make you explore the language and the documentation a little. In this case read perlvar to gain a little insight. ;)

---

DWIM is Perl's answer to Gödel