I am trying to scan a SharePoint site but I am getting User scan-user does not have permissions to scan http://some-sharepoint-site/.
When I connect to the same SharePoint site using a browser, I am able to do so without any problems. What can be causing this?

This is a permissions issue. A user who can connect to a SharePoint site with a browser may not be able to scan it using a discover scan.

When using the browser a user with 'read' permission level is able to read the contents of a SharePoint site. However, when running a discover scan,
the scan starts from the 'root' level URL that the user has entered as the target. At this level, 'browse directories' permission is needed.

This allows the user to retrieve a listing of all folders and items present in the site. Therefore, a user who can connect to a SharePoint site with a browser, may
not be able to scan it using a Discover scan. The least privileged permission level with the 'browse directories' permission is the 'contribute' permission level.

Either assign the user to a group with that permission level or explicitly grant just that user the necessary permissions.