This question has a fairly obvious answer. Your cat is trying to get to the other side of the door of course. When you need to leave a room, you use a door so it shouldn’t come as a surprise that your cat is mimicking your actions.
Cats are smarter than people give them credit for. They can often learn new tricks and behaviors just from watching someone. If this behavior bothers you you could try installing a lock, changing your door handles to the round knob style, or bribing your cat with large amounts of food. If that does not work, there is always the option of twenty-four hour cat surveillance .
We recommend constant vigilance when it comes to the front door of your house; a runaway cat is never a good thing!