In Type I diabetes, amyloid fibrils emerge spontaneously during the growth of insulin from recombinant DNA technology. This is a problem because you have to disentangle the fibrils to produce useful insulin for the diabetic patients!
In Type I, the insulin or its precursor proinsulin becomes, for reasons due to some shock to the system or inheritance, viewed by the body as a germ element, and an autoimmune response attacks the beta cells of the pancreas to shut off insulin production.
In Type II diabetes, amyloid fibrils of the protein amylin are formed, and through as yet unclear reasons, these trigger programmed cell death of the insulin producing beta cells.
Either way, insulin production is shut off and the necessary signals for metabolism of sugar are messed up!