Henock,
Yes, normal users need Author rights with Create so that they can create Leave Requests.
Only System Administrators, like yourself, need Delete rights.
The sole purpose of the button is so that one person can request leave for another: such as an Administrative Assistant for a Manager. When the Request is saved for the first time a message is mailed to the named Requestor and the Approval Manager. If there is any problem with the request then it can be deleted or denied.
The person who created the request is named in the Edit History at the bottom of the Leave Request and is also saved in the $UpdateBy field. If someone is feloniously entering Leave Requests, then their Manager needs to be informed so that appropriate action can be taken.
If you do not want a button in your application, then just delete it from the Leave Request form and you will not have it.
HTH,
Bob