Pretty simple.
On every system, windows 7 the default first user should be an admin.
In order to promote another user to admin elevation the first or original Admin account must be used.
Once you have elevated another account to admin. You can then remove or delete the other Admin account.
Log out of the first admin account, log into the new one
and delete the other admin account. or change it`s type.
It`s permission rights.
In other words an admin of the account cannot delete the admin account when logged into it if his own.
But another admin of another account can.
Since always one has to exist.
So why you cannot delete an admin account is because your using the actual account selected to delete. Logged into it. Its in use.
You have to make sure you log out of one, and log into to another.
One admin account must always reside.
Use windows account manager.