home default category

Untick the “Home” category when writing the post?

I think you’re confusing things here. Having a ‘Home’ category does not equal the home page. “Home page” is just what we call the entry page to your blog (also referred to as the “front” page). It has no relation to a specific category, at least not without customizing on your part.

See this plugin for one solution:

http://dev.wp-plugins.org/file/front-page-cats/trunk/front_page_cats.php

(scroll to the bottom of page and click “original format” to download)