What's tripping you up is the </script>. The HTML parser doesn't recognize Javascript strings or nested <script> tags, so it's interpreting that as the closing tag for the initial <script>. That is, this part of the document is parsed as:
<script> (open tag)
alert("<script> (text node - contents of the script)
</script> (close tag)
"); (text node - plain text)
The second </script> is ignored, as there's no other <script> tag for it to close.
To work around this, break up </script so that the HTML parser doesn't see it. For instance:
alert("<script></script>");
or:
alert("<script><" + "/script>");
or just put the code in an external Javascript file. This issue only arises for inline scripts.
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