First, what does doing this buy you that using diff doesn't? Use the right tool for the right job.
Second, You will want to use a hash, not an array. (I'm abbreviating here. Add the excellent fileopen stuff you're doing.)
chomp( my @first = <FIRST> );
chomp( my @last = <LAST> );
my %last_names;
undef @last_names{ @last };
foreach my $name (@first ) {
next if exists $last_names{ $name };
print "$name\n";
}
Being right, does not endow the right to be rude; politeness costs nothing.
Being unknowing, is not the same as being stupid.
Expressing a contrary opinion, whether to the individual or the group, is more often a sign of deeper thought than of cantankerous belligerence.
Do not mistake your goals as the only goals; your opinion as the only opinion; your confidence as correctness. Saying you know better is not the same as explaining you know better.