There's any number of reasons ranging from "This website is not vulnerable to XSS" down to "You need to massage your XSS string some more".
Getting XSS popups to work is a bit of an art. The Inspect Element view is not the best way to look at it because that is showing how your browser has parsed the HTML, but the whole point of XSS is to fool the HTML parser.
Instead do View Page Source and ctrl+f for your string
alert("XSS"). First, as @Sjoerd suggests, see if your string is being escaped (ie do you see
<script>?). If being escaped properly, then you won't be able to do XSS. If it's not being escaped, then there probably is XSS. To get it working, you'll need to look at where your text is being placed within the source and close any strings and tags so that your
<script> tag is not buried inside something else. That's why you often see XSS payloads start with a quote and a close-tag, like
"</a><script>.... This part takes some trial and error. Good luck!