Question: When asking around, I've never heard anyone agree that a young, healthy person should end their life by suicide. But I also don't know what reason there is for that consensus. 

Did Buddha teach anything regarding what makes life worth living?

Answer: 
You shouldn't even think about things like suicide. Thoughts will be full of negative emotions and states that it will drag you to lower planes. 

When you are doing the act you will have negative thoughts which would mean that your next life is bad.

You are also breaking the precept of not killing which is very grave. 

Also it is best you see a doctor but until then practice Metta to your self and others.
The following only is relevant if you follow Buddhism\ the following are all from Shantideva's text: 

1. "Upon finding the boat of human birth now, cross the great river of suffering. O fool, there is no time to sleep, for this boat is hard to catch again."
2. When shall I encounter the extremely rare appearance of the Tathagata, faith, human existence and the ability to practice virtue,
3. Health , daily sustenance, and lack of adversity? life is momentary and deceptive; and the body is as if on loan.
4. With such behavior on my part, a human state is certainly not obtained again. When a human state is not achieved, there is only vice. When a human state is not achieved, there is only vice and how could there be blessing?
5. If I do not perform virtue even when I am capable of it, what then shall I do when fully dazed by the sufferings of miserable states of existence
6. For one who does not perform virtue but accumulates sin, even the expression "favorable state of existence" will be lost for a thousand million eons.
7. Therefore, the Blessed One (Buddha) stated that human existence is extremely hard to obtain, like a turtle's head emerging into the ring of a yoke on a vast ocean.

The text goes on and on. Too lazy to type the rest. I'll leave you with one of my favorite lines:

"Enemies such as craving and hatred are without arms, legs and so on. They are neither courageous nor wise. How is it that they have enslaved me? " 

-If you are a Buddhist and accept certain Buddhist ideas and thoughts then the above may help answer your question.