The option to "show on home page" is a little confusing if you have your blog set up to show a static home page with your main blog page as a different page. In this scenario, checking this option will show the addthis button on posts on your main blog page, not your home page (which is a static page).
You can use is_front_page() to detect if it is the home page of the site, even if this is a static page. The is_home() function detects if you are on the main blog page.
It it worth adding the option to show on main blog page to differentiate in this circumstance?