A Pushmi-pullyu in Middle Earth!?!

[alatar]

A Pushmi-pullyu, an animal in the Hugh Lofting's 'Doctor Dolittle' books, has the front sections of two animals connected at the middle. When it tries to move, it has trouble as both heads go in opposite directions, resulting in it going nowhere. This animal has yet to be seen in Middle Earth, even in the movie adaptations. That said, there is a reference to a different kind of 'push me - pull you' in the LotR. Where? Well, in the the Chamber of Mazarbul in Moria.

This has always bothered me. When the Fellowship is caught unawares by the orcs after 'Gandalf's story time,' the following is stated about the door between the company and the enemy:

Originally Posted by Aragorn

"We can't block the door. The key is gone and the lock is broken, and it opens inwards."

Why is this not a good thing? I would think that a door opening inwards would be easier to hold closed. Sure, the enemy would have maybe an easier time pushing the door inward, but, using wedges as the Fellowship does, it would seem that this type of door swinging would be preferable to the defense than the other orientation.

How would one easily defend a door that pulled open?

So I think that Gandalf must have been just letting us know the layout of the room, and not making any negative comment about the door being a push me-pull you.