Try adding the index to the file name and closing the file inside the loop. Right now you are over-writing the file each time.

for (my $i=0; $i<@array1; $i++)  {
          open (OUT, ">$$.out.$i") or die "can't open OUT\n";
          print OUT ">$array1[$i]>$array2[$i]\n\n\n";
          close(OUT) or die "Close error on $$.out.$i -- $!\n";
}
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