For a non-destructive method that leaves the original array intact (we use a modulus flip-flop):

for my $i ( 0 .. $#in ) {
    $i % 2 ? push @out2, $in[$i] : push @out1, $in[$i];
}
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I fail to see where the "either side" comes from.... If you mean your array is:

2022, 2002, 6, 78 1023, 1232

Then the following should work:

while( @in ){
  push @out1, shift(@in);
  push @out2, shift(@in);
}
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This C style approach is 50% faster than the push approach posted earlier. Ugly but fast.

use Benchmark;

@in = (1,2,3,4,5,6,7,8,9,0);

timethese ( 100000, { 
    'C-style' =>
            'for my $i ( 0 .. $#in ) { 
                $i % 2 ? $out2[int($i/2)] = $in[$i] : $out1[$i/2] = $i
+n[$i] 
            }',
    'push'  => 
            'for my $i ( 0 .. $#in ) {
                $i % 2 ? push @out2, $in[$i] : push @out1, $in[$i];
            }' 
        } );

__DATA__
Benchmark: timing 100000 iterations of C-style, push...
   C-style: 13 wallclock secs (12.97 usr +  0.00 sys = 12.97 CPU) @ 77
+10.10/s (n=100000)
      push: 18 wallclock secs (18.79 usr +  0.00 sys = 18.79 CPU) @ 53
+21.98/s (n=100000)

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$|-- ? push @a, $_ : push @b, $_ for @in;
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This looks similar to Can I multiply corresponding numbers in two arrays together?.

Skipping one element can happen with a next in your loop, or just increment the index, if you are using them.