I should note that if you research Immunogenetics you should find alot of theories.
I'm not sure of your clinical background or how your knowledge understands the breakdown of T cell destruction and/or regeneration but this article and it's reference material can show you more about the T cell seperation and why autominnue thyroid is associated with certain other autoimmune conditions.
http://www.jautoimdis.com/content/2/1/1
The latest study i have come across shows 16% with Hashimoto's thyroiditis had another autoimmune disease and of those 16% a quarter had yet another autoimmune disease. The most frequent associated diseases (1541 patients) was chronic atrophic gastritis (34.8%), nonsegmental vitiligo (22.3%), celiac disease (11.0%), antiphospholipids syndrome, and multiple sclerosis (7.6%).
About 10% (overall mean age 39 years) were diagnosed before they reached the age of 30. The most frequent diagnoses were vitiligo (39%), celiac disease (26%); chronic atrophic gastritis was not as common (13%).
Patients with both types of autoimmune disorders were more likely to have thyroxine malabsorption, chronic unexplained anaemia, and recurrent pregnancy loss than patients with only Hashimoto's thyroiditis. You can read the full article on Medscape - "Thyroiditis Often Linked to Other Autoimmune Disorders".