From the article: “I don’t mind a bit being labelled a suicide.”
By continuing to use the word suicide for people who chose assisted death you make it harder for people to get assisted death legalised.
Assissted dying is when you ask a doctor to kill you, or to help you kill yourself.
It's useful to seperate out people who want to control their death when they have an incurable illness from people who want to die when they have a treatable mental illness.
It's especially useful if you want assisted death to become legal. It makes it a bit clearer that you're not trying to make it easier for people with mental illness to die.