Some people use the label "mentally ill" as an insult or out of ignorance, this seems to be especially true for "unstable." I think it's impolite anyway regardless of intention. I am not a "mentally ill/unstable person", I am a person with mental illnesses. I am a person first.
I take issue with the term "mental" illness altogether, because they are taken less seriously than "physical" illnesses. They are physical - they are illnesses of the brain that impact many different areas, including our nerve cells and gray matter. The term "mental" implies to me that these conditions "just happen" in a vacuum, and are treated as inconveniences we can positively think our way out of. Imagine the potential shift in culture if it was labelled a brain disease or illness instead.
I would also contest that society itself is "unstable." They point the finger at us but look at how broken it is. Look at how people who struggle with wanting to die are treated. Look at how the abused, the poor, the homeless, migrants etc are treated. Look at the healthcare system, the class and welfare system, the way things are governed, the way everything is catered to the "mentally stable", able-bodied, "normal" working 9-5 folk. Look at how anyone who does not fit into this neat box is treated. I may struggle with various illnesses - both of the brain and the body - but in some ways I see more clearly how profoundly wrong this is than those without my experiences, who often blindly partake in this catastrophic, cutthroat system. See how discrimination, ruthlessness, money and ostracism underpins the way modern society functions. Society is sick.