I am sad that the best answer a graduating student can give you is "the mouth is different". If that was all I had to go on, I would think its full of crap too. Let's see if I can give a better explaination.
(I will keep this simple, I can go into more detail if you would like)
The body fight infections with the immune system cells. When an area is infected, it sends out signals for increased blood flow to the area and these cells to respond. The cells, in amazing order, leave the bloodstream and enter the infected tissues to fight off the infection. As you can imagine, cells have their own size and mass, and when many invade the area they fill up. This is why infected areas turn red and swell, increased blood supply and immune combat cells.
Bacterial growth also leads to swelling as well on its own.
Now, to the difference. Most of your body can expand and contract fairly easily to a point. Skin, connective tissue, and blood vessels all have elastic fibers. So the swelling caused by infections and the body's response does not cause a problem. However, the tooth is a small, confined space, with no elastic ability. In addition, the only entrance and exit to the pulp tissue is through an extremely small hole at the end of the tooth. At a tooth's full maturity, this apex is just large enough for a small blood vessel and the nerve. There is no room for the vessel to expand to bring the necessary increased blood flow necessary to fight infection. The pulp chamber cannot expand to allow enough necessary immune cells to infiltrate the tissues. And any swelling inside the tooth will increase pressure within the tooth, and since all blood flow is based on pressure, there comes a point in a tooth's infection that the flow will stop completely, leaving stagnant blood and no new oxygen, immune cells, nutrients, or anything else necessary for the body's normal infection control. The tooth ends up dying from the untreated bacteria, the pressure buildup, or the lack of necessary blood/oxygen flow.
I hope that was a little better explaination than you were given.