The code above explains the output perfectly. I think you really mean something more like:

while(<F1>)
    my $ok = 0;
    for my $tag ( @tags )
        $ok = /^\s*(\<$tag\>)(.*)$/ and last;
    }
    $ok or die "Incorrect entry $_";
    # $1 is now the tag, $2 the rest of the line
    # ...
}
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I changed the code a lot because I couldn't find a simple adjustment to get the OP to do this.