While removing entries from an array like that is inadvisable, your code will not work as expected for two reasons:

1. You only increment $arrayCounter after a delete, when it needs to be incremented on every loop.
2. After a delete, on the next main loop, you attempt to reuse the deleted array element.

The following should work as you expect:

foreach my $currentremotefilelist (@remoteFilelist)
{
    my $arrayCounter = -1;
    foreach my $currentlocalfilelist (@return2)
    {
        $arrayCounter++;    # Increment on every loop iteration

        next if !defined $currentlocalfilelist;       # Skip previousl
+y deleted entries

        #myfile.txt =~ myfile.txt_date
        my $currentremotefilelistsize = -s $currentremotefilelist;
        my $currentlocalfilelistsize = -s $logSite.$currentlocalfileli
+st;
        $currentlocalfilelist = $logSite.$currentlocalfilelist;
                
        if (($currentremotefilelist =~ /^$currentlocalfilelist/i) && (
+$currentremotefilelistsize == $currentlocalfilelistsize))
        {
            print "$currentremotefilelist and $currentlocalfilelist al
+so $currentlocalfilelistsize and $currentlocalfilelistsize They are E
+qual and will not be copied\n\n";
            delete $return2[$arrayCounter];
        }
        else
        {
                print "$currentremotefilelist and $currentlocalfilelis
+t also $currentlocalfilelistsize and $currentlocalfilelistsize are no
+t EQUAL!!\n";
        }
    }
}
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Updated: moved counter to above the next