So if I understand you, you are saying that you created  a contacts  List
with entries  for your users  in it, and that a user  cannot edit  the
entry for him or herself? If that is what you are saying, then that is
expected behavior. SharePoint looks at the creator of the Contact, not
the person  whose information is in the Contact, when evaluating whether
they can edit it. So if you made all the contacts, and you set the
permissions so that people can only edit their "own" items, this means
that only you can edit it.

You would be better off creating a Content Query web part that displays
existing profile information, since this information can be configured
so that users can only edit information about themselves.

I actually had this "problem" with
two types of lists - tasks and contacts. You understood my
situation correctly -- I created  the contact and task entries  and
expected others to be able to edit  them based on the fact that their
login name was in the "assigned to" field (tasks) and "Login" field
(contacts). In effect, I assumed that the entries in these fields
drove who could edit the entries, not the creator of the records.
Obviously, I misunderstood the intent of the functionality  and I'm
included the explanation above in case anyone else has the same
misunderstanding in the future.

By "Edit Their Own items", the system means that users  can edit  items
they created. If users did not actually create a record of their own
account information, and someone else seeded the list  with everyone's
contact information, then only the person  who uploaded the original list
information would be able to make changes.

can i do the same thing with a document library.
I have differerent users  uploading their docs. I don't want the same file number
uploaded how can i prevent that.