Understanding file security model (or Why Can't I Access That File??)

1. Folder_1 has access rights which include full access to the Administrators group.
2. I'm logged in as User_A which is a member of the Administrators group.
3. When I try to open Folder_1, I get the message, "You don't currently have permission to access this folder. Click Continue to permanently get access to this folder."
4. If I click Continue, User_A is added to Folder_1's permissions list with full rights.

So, first of all, why am I not simply allowed to access the folder in step 3?

Secondly, doesn't adding explicit permissions for User_A in step 4 override the benefit of using securitygroups rather than individual user accounts when assigning file system rights?

Amongst other problems, if I remove User_A from the Administrators group, the user will still have access to this folder!

Someone please explain the logic here, or what the right way to assign these rights would be.