Why is assisted suicide illegal?

It is legal in many states. Move to one of those.

Five states and the District of Columbia have passed laws legalizing assisted suicide in certain limited circumstances. Under Oregon's Death with Dignity Act, physicians can prescribe lethal medication that will allow terminally ill individuals to end their lives.

It isn't universally illegal. Canada moved to legalize in in small doses. It is complicated though because when people get to the point they might figure it's best to just die, they're often not in a state of mind to make that decision - at which point it's a question who can. My grandmother had Alzheimer's for 13 years - by the time she lost her mind to the point daily living was basically pointless, she clearly wasn't in a position to sign off on assisted death. People will have to write up a living will that dictates very specifically under what circumstances they want to refuse medical treatment, and when it is best to end life. That gets legally hairy quickly.

Why does it need to be 'assisted?' Why turn another human being into a murderer, legally sanctioned or not, because you simply don't have the stones to do it yourself?

Willful self-destruction is generally frowned upon by people of conscience, at any age. Believe it or not, sitting and quietly contemplating the life you have lived can be quite enjoyable for the old. Contributing to the futures of others can be also. If you are willing to kill yourself because it is a long trip to the bathroom or you need to pay someone to wipe your rear end, you are a selfish dingbat.

Ask your politicians. i watched my Mom and Dad pass, both were ready to go much earlier then they did. Currently, I am a stay at home husband to a mentally and physically damaged mother in-law. It's tough, but needed. At the end of a day, good or bad, I sure do appreciate a quality of life now.

But what if some member of your family just thinks you are unable care for yourself?

No, you wouldn't. You're just a young fool. If you were 75 years old and unable to care for yourself, you'd want to live and have people care for you.
It's really easy to say "if (fill in the blank" but if you pose the question to people for whom it's a remote possibility you get completely different answers from those for whom it's a more imminent possibility, or a reality. This topic has been studied fairly extensively, and results are consistent.