Why can't I log in to SYSTEM without AS SYSDBA
Because you are not logged in as the user system. When you execute conn system/password as sysdba, Oracle won't even check the user and password (--> from the local systeem where the db is running on). If you enter the system/password as sysdba and then execute 'show user', you'll notice you are logged in as user 'SYS'. So you are actually entering the wrong password when you execute the conn system/password, Oracle doest not lie.
Check http://docs.oracle.com/cd/B28359_01/server.111/b28310/dba006.htm#ADMIN11046 for more information. Because what I told you is not the whole story.