Hi,
The default Editor in Joomla strips some HTML tags like this case.
Before editing custom HTML module like this, try going to Global Configuration > Site tab > set Default Editor to None first.
Then edit this module again.
Here is the output of head social module as in our demo site:
<ul class="social-list">
<li><a class="facebook" title="Facebook" href="https://www.facebook.com/joomlart"><i class="fa fa-facebook"></i></a></li>
<li><a class="twitter" title="Twitter" href="https://twitter.com/JoomlArt"><i class="fa fa-twitter"></i></a></li>
<li><a class="google-plus" title="Google plus" href="http://www.joomlart.com/"><i class="fa fa-google-plus"></i></a></li>
<li><a class="youtube" title="Youtube" href="http://www.joomlart.com/"><i class="fa fa-youtube"></i></a></li>
</ul>