One gives you a choice, the other one doesn't. If you want to prevent abuse, make it difficult in the law. Restrict it to advanced directives, require a psychological assessment, etc.
The scenario you're describing is the easy one — if I have people who love me enough that they're willing to care for me, I wouldn't feel forced into making this decision and there's no risk of abuse. If anything, I might feel pressured to stick around to avoid hurting them.
GP's argument is trickier: Callous family members might want to force me into accepting assisted suicide against my will, because they don't want to care for me. My point was precisely that, in that position, I wouldn't want to be cared for by those callous relatives, and might choose assisted suicide of my own accord anyway.