Why does a tooth abscess not spread and cause an infection of the other teeth?

It can: A tooth abscess can spread and cause an infection on another tooth next to it. This isn't common though.

Not entirely true: Tooth abscess can spread to the adjacent teeth causing these teeth to be affected. However, the majority of the time, the infection drains into the adjacent soft tissue causing them to swell.

You're right...: Most tooth abscesses rarely affect adjacent teeth. This is a remarkable sign of a healthy immune system that can hold the infection 'at bay.' the infection tends affect the supporting bone and not destroy blood supply or nerves. If the cause of the infection is removed (extraction or root canal) our bodies can heal the affected bone while the blood/nerves still survive. Amazing isn't it?

Nice question...: The other teeth are protected by a healthy blood supply entering the tooth. The infection cannot pierce through those blood vessels. However, the abscess can spread through your face and even down to your heart. Abscesses must be professionally treated every time to prevent serious harm as much as possible.

Rare: On rare occasion, an untreated tooth abscess will involve an adjacent tooth. If the abscess is in the gum and bone in periodontal disease, the infection will spread to other teeth. Untreated periodontal disease causes tooth loss and the inflammation that goes along with it can be a factor in increased risk of heart attacks, stroke, diabetes, cancer, alzheimers, and adverse pregnancy outcomes.

Anatomy: Infections tend to spread through path of least resistance. They spread more readily through soft tissue, blood supply, lymphatic system, fascial planes, etc, rather than through hard structures such as bone that separates the teeth. Furthermore, the infection would have to enter into the blood supply of the tooth which is housed in hard tooth structure and take hold-very, very unlikely.