My theory:

Red John is not a member of the secret tyger tyger society, but knows about it and possibly started it. Therefore they are afraid he will be caught because it will bring out their secrets. Partridge was a member of the tyger tyger society, and so are all the other suspects on the list, except Kirkland obviously, and Stiles (because he is not law enforcement). RJ murdered Partridge as a warning to the others, so they won't give him up.

Also it makes sense that a weak person like Michael Kirkland would fall in the hands of Stiles through Visualise.