Before this rule all tracks AND rolling stock would be owned by single, national entities in every country. If you were a Austrian train operator wanting to run trains to Germany you'd have to ask Deutsche Bahn for space on the rail, and they would (obviously) give priority to their own rolling stock.

This would happen to the point where it was almost impossible to organise cross border rail connections.

By seperating the track from the train you can make the train companies compete with each other on a (more) equal footing.

Ironically, most of the 'private' train companies now running on UK tracks are actually Dutch, German and French state owned railway companies competing with each other.