That your reasons are important to you means they are reason enough. However, if their points seem sound, giving their way a try might be a worth a shot. As [NoName] says, you don't have anything to lose. Give it a fair shake and see what it nets you. After all, you're not forever giving up the option to ctb.
Do I have a similar situation? Maybe. It's hard to say. I think a lot of us probably do, if we're completely honest. Dig in and give more than we think we have, or even just more than we want to give, and seek a way out? Why, when we want to die? Hell, I don't know. Dying is a hell of a lot simpler, I do know that. When you hope the light at the end of the tunnel is an oncoming train, so you can step in front of it, discovering that it might be the way out, after a long, long slog, can be disspiriting.
I know I want to die. I can sure sympathize with you on that!
I don't know your situation. I don't know how old you are, and whether you might have enough life left to you that the investment in effort is worth it. I don't know if you have the remaining reserves for the work it might take you to climb out of the pit.
But if you're considering your parents' option, I'd strongly suggest you take it.