The mature way to handle suicidal people is to call professional help, as soon as possible. If the suicidal thinking is caused by some kind of hormonal imbalance -- which the person will report as "I have logically concluded that it is better for me to die", because that is how it feels from inside -- you cannot fix the hormonal imbalance by a clever argument; that would be magical thinking. Most likely, you will talk to the person until their hormonal spike passes, then the person will say "uhm, what you said makes a lot of sense, I already feel better, thanks!", and the next day you will find them hanging from the noose in their room, because another hormonal spike hit them later in the evening, and they "logically concluded" that life actually is meaningless and there is no hope and no reason to delay the inevitable, so they wouldn't even call you or wait until the morning, because that also would be pointless.
(Been there, failed to do the right thing, lost a friend.)
Sure, this seems like an unfalsifiable hypothesis "you believe it is not caused by hormones because that belief is caused by hormones". But that's exactly the reason to seek professional help instead of debating it; to measure your actual level of hormones, and if necessary, to fix it. Body and mind are connected more than most people admit.
That's all from my side. If you are sincere, I wish you luck. Any meaningful help I could offer is exactly what you refuse, so I have nothing more to add.
The mature way to handle suicidal people is to call professional help, as soon as possible.
It's worth noting that this creates an incentive to never talk about your problems.
My advice for people who value not being kidnapped and forcibly drugged by unaccountable authority figures who won't listen to reason is to never voluntarily talk to psychiatrists, for the same reason you should never talk to cops.
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