I agree with Generoso and sundialsvc4 on the use of grep. Although, I would use the BLOCK form of grep in keeping with PBP Chapter 8, "Always use a block with a map and grep." Like this:

use strict;
use warnings;

open my $fh, '<', 'hosts' or die;
my @hosts = <$fh>;
close $fh;

my @new_hosts = grep { !/$ARGV[0]/ } @hosts;

print "\nnew_hosts:\n";
print join "", @new_hosts;
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However, this does not address your desire to print the excluded lines. For that, you could do this:

use strict;
use warnings;

open my $fh, '<', 'hosts' or die;
my @hosts = <$fh>;
close $fh;

print "Excluding these lines:\n";
my @new_hosts = grep { print $_ if /$ARGV[0]/; !/$ARGV[0]/} @hosts;

print "\nThe new array:\n";
print join "", @new_hosts;
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But at that point, maybe your for loop might be clearer.