As the creator / owner of the directory you have full permissions for the account you are logged into. The webserver runs on a different set of permissions as a system process...
Therefore you have to allow the system process (which is like another user logged into the machine) permission to perform the same actions you are discussing.
Hope that makes sense. This is just the way security is set up through most web servers (include MS based, apache, etc) that I know of. Permissions are generally based on the directory sometimes inherited from parent directories. Access priveleges for specific accounts are usually toggled on and off. For web server type applications the permissions generally start fairly high to keep your machine running securely. Otherwise someone could use your web server to run malicious scripts on your machine (I.E. hacking there are often holes that are utilized to do this very thing). It is generally up to the server administrator to give the web server directories permissions to perform system type task outside of processing files that lie in the directory structure to push out to a client. Anything that causes the machine to run machine level actions (moving / updating / executing files) is generally restricted. The usual place that things of this nature can occur would be in tmp directories or CGI directories.
In order to allow or override you have to play with the permissions. This doesn't generally get set up out of the box. You could always attempt to login as the process (although I don't know how to do this) and see if you can perform the move action to test.
However when messing with permission be very careful as you could allow for exploits depending on how you do it. I would suggest playing with these after some reading and then testing on a development server before you expose this type or issue to the general population.
Hope that helps,
Geoffrey