Sharepoint 2013 – unable to hide a subsite from navigation

That depends - A list and a site hold very different content. Your navigation shouldn't dictate your content. It should be the other way around. A list describes related items, whereas a site is a container for many lists, document libraries, etc.

We have 2 ways to do this.

Method 1:

1. From the Snippet Gallery, copy and paste the default SiteLogo code snippet into your master page into the appropriate place you want it to be displayed.

2. In the SiteLogo code, search for SharePoint:SPSimpleSiteLink to find the relevant opening and closing tags. Now simply change the tag names to SharePoint:SPLinkButton instead.

3. Then simply add the attribute NavigateUrl to this tag and set it’s value to “~sitecollection/”.

Example:

Default snippet code:

<!--MS:<SharePoint:SPSimpleSiteLink runat="server" CssClass="ms-siteicon-a" ID="x7917ecc8c38d4bd69f58e338eab54c8c">--> ... <!--ME:</SharePoint:SPSimpleSiteLink>--> Should become this:

<!--MS:<SharePoint:SPLinkButton runat="server" NavigateUrl="~sitecollection/" CssClass="ms-siteicon-a" ID="x7917ecc8c38d4bd69f58e338eab54c8c">--> ... <!--ME:</SharePoint:SPLinkButton>-->

Ref link

Method 2:

We are going to add custom js in the master page => our site is a publishing site

We find the site logo in the below hierarchy(in a rendered page).

    <div id='DeltaSiteLogo'>
        <a href='site url'>
            <img src='siteIconPath.png/whatever extension'/> 
        </a>
    </div>

So we may try the following for redirecting to the site collection/root web url on click of the logo.

// Add the following js in the '.html' design file that associates with the corresponding masterpage.

    <script type="text/javascript">//<![CDATA[
    $(document).ready(function(){
      $("div#DeltaSiteLogo a").attr("href",_spPageContextInfo.siteAbsoluteUrl);
    });
    //]]>
    </script>