In a few words, the cause of cystic acne is multiple ruptures and re-encapsulations. Let me explain

Cystic acne starts as normal acne:

During the increased oil production of puberty, sometimes a sebaceous follicle becomes hyper-keratotic, meaning the follicle becomes hardened with the same kind of dead skin cells as the skin's surface. Scientists are sure why this happens, but they believe the increased levels of oil somehow irritate the follicle. 

If the top of the follicle, or "pore", stays open, it becomes a blackhead, but if the top of the follicle closes, it becomes a whitehead. Due to the increasing pressure inside the white, sometimes the follicle wall ruptures and releases its contents into the surrounding tissue, leading the body to initiate a foreign-body type response including swelling, pain, and redness. 

At this point in the process, I would still call this a "normal" zit. Most noticeable whiteheads include some level of swelling and redness, indicating they have undergone at least one rupture and re-encapsulation. If the process stops here, the whitehead might become a firm papule for several days, but the immune system will soon liquefy the contents of the capsule making it easy to pop and heal.

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For some reason, also unknown to scientists, some people's acne undergoes an unfortunate, two-part process:

First, they tend to have acne that frequently ruptures on the deepest surface so that the contents spill deep in the cutis or subcutis. The immune system is not able to liquefy foreign contents this deep in the skin because they are too far to be pushed to the skins surface and would become toxic, so the immune system must slowly breakdown the foreign material and carry it away through the blood stream.

Second, they tend to have an over-active immune system response. Once the follicle ruptures, the body tries to encapsulate the material. In most people, this process is successful, but in cystic acne sufferers, the body sends too many white blood cells into the capsule causing it to re-rupture. When this happens, the body will try to re-encapsulate the material. The process of rupturing and re-encapsulating becomes a vicious cycle causing the zit to grow larger and to never heal.

Acne breakouts are basically the result of hormones and genetics, meaning acne sufferers haven't done anything to cause and shouldn't be ashamed of their acne; this is especially true in cystic where the body's overly aggressive immune response is much like an allergy.

On the negative side, though, since there's nothing the cystic acne sufferer did to cause their cystic acne, there's frequently nothing they can do to cure it without seeking medical help. its important to seek medical help as soon as possible because acne cysts are much easier to prevent then to cure and earlier treatment helps prevent scarring.