OOTB SharePoint will not allow you to remove the 1st tab on the main navigation through the UI. To do this you can simply use the following CSS below and add it to your custom CSS or use the CEWP page style method to just make the change just for that page.
If you look at the code, you will notice that each top navigation item has an ID.
- zz1_TopNavigationMenun0 (Home Tab)
- zz1_TopNavigationMenun1 (Tab #2)
- zz1_TopNavigationMenun2 (Tab #3)
- zz1_TopNavigationMenun... (Tab Etc)
Since the home tab is always #1 it is always given the ID of "0"
display: none !important;