The strong will to live inherent in most humans means that suicide is typically not a choice people can make. That's kind of my whole point: the fact that anybody can ever make this choice is remarkable. But to take the possibility of suicide and thereby declare that suffering is a choice makes no sense to me. It may be for some, but not for most.
You did see that I listed other options, right?
Does it matter? There are plenty of people suffering from problems that can't be fixed by pills or therapy and who are not mentally capable of suicide. Suffering may be a choice for some, but it is not a choice for many.
Many people choose not to suffer, because "suicide is an option". Or pills. Or therapy. Or, the lucky ones, they can switch it off.
Depression (noted in another comment) further limits the ways by which one can control the suffering brought on by pain. I know this well. Many of us do.