Aging is a slide into disease state. A non-healthy or misbehaving cell is in a disease state. Accumulation of intracellular and extracellular garbage, DNA point mutations, transpositions, malfunction of the cell cycle, abnormal signalling, and a myriad of other break downs are disease state.
Cells are machines and they function in predictable biomechanical and biochemical manners. Aging related disease state encompasses some population of the space of deleterious state change.
In the micro, aging is a disease just like any other. It is the layperson understanding of the word "disease" that does not fit.