This is an unbelievably slippery slope. It has the potential for great good, but also for great harm. Cliched and click-bait phrases, but I believe they are accurate in this instance. I'll try to explain why I believe that.
A case has been made that Facebook users are not the customers, they are the product, and that data purchasers and advertisers are the customers. If Facebook can determine whether you are suicidal then it might determine other psychological conditions such as agoraphobia, alcoholism, depression, ADD, SAD, etc.
Once that determination is made and stored the possibility exists that it could be hacked or exposed in a data breach.
The possibility also would exist for Facebook to sell that information, and/or to target users with medical adds related to their condition. I am not saying Facebook would do this, I'd like to think they wouldn't - I have friends at Facebook, though they aren't in management.
However, the decision of whether to allow this has to be based not on whether it's safe to trust Facebook with this information, but on whether it is safe to trust any company with it.
What happens if there is a false positive for suicidal tendencies or another condition?
Take this to the absurd extreme and consider how it compares to the Pre-Crime operations depicted in the movie Minority Report. Instead of Oracles we have Machine Learning intelligent software agents. Most of the problems depicted in the movie could arise.
To a lesser extreme, imagine the situation when a false positive occurs for a user in a position of public trust, a government official, or a defense contractor with a clearance. I'll assume this triggers action in some way that is visible to some combination of the user, psychology professionals, authorities, and an employer - otherwise why do it. If the employer in any way catches wind of the determination they might very well take steps to flag and/or terminate the employee.
Even if the employer doesn't flag the employee or terminate them, if the information is purchasable or discoverable in any way then an insurance company could conceivably raise the user's rates based on the determination.
I am all for advancing technology, especially in the field of AI, but when we apply that technology we need to ask not just if we can use the technology in that way, but also if we should.