How do these sites know what framework I'm using and how do I hide it?

Builtwith can recognise CodeIgniter based on the directory structure (and index.html files in every dir) afaik.

If they can see the directory structure of your site and the index.html files in those directories, you've probably got bigger things to worry about than whether they can recognize what framework you're using.

They not see anything on my sites, I don't have application and system folders and I use .htaccess rewrite rules to prevent access.

I think you may be right about cookie tracking. I have old sites with the default cookie name and they are recognised by builtwith but if I try out other sites with different cookie names then builtwith cannot recognise the framework.