Suicide debate

Person 1: My friend has been feeling suicidal so she is going to see a psychiatrist.

Person 2: Risk of suicide increases after consulting a psychiatrist.

Person 1: Of course, suicidal people would be more likely to go to a psychiatrist, just as you would find a lot more cavities in people going to the dentist.

Person 2: True, but there should be less cavities in the group of people who previously consulted a dentist than among those who didn't. If psychiatry worked for suicidal people, there would be less suicides in the supposedly treated population than in those who never sought help from psychiatry. Either it doesn't work or it makes things worse.

Is anyone commiting a fallacy here?

Person 2: Risk of suicide increases after consulting a psychiatrist.

Person 1: Of course, suicidal people would be more likely to go to a psychiatrist, just as you would find a lot more cavities in people going to the dentist.

Person 1 missed the point (ignoratio elenchi). They were trying to say that there is a correlation between people being suicidal and going to a psychiatrist (which isn't unexpected - the type of people to need psychiatrists will typically be struggling with one or more mental health issues, which suicidal people usually are). But the person they were responding to was saying that the risk of suicide increases after visiting a psychiatrist. I might be reading too much into this but it seems like they're talking past each other here.

We're going to need a source for person 2's claim, by the way. It's pretty contentious. They'd have to give some solid evidence.

Person 2: True, but there should be less cavities in the group of people who previously consulted a dentist than among those who didn't. If psychiatry worked for suicidal people, there would be less suicides in the supposedly treated population than in those who never sought help from psychiatry. Either it doesn't work or it makes things worse.

What does 'consulted a dentist' mean? Did they actually have dental work done or not? Because if you simply 'see' a dentist, but don't actually undergo any procedures, then that's as good as nothing when it comes to fixing any problems to do with one's teeth (e.g. cavities). Thus, you could have a group of people that 'consulted' a dentist but still have cavities. On the other hand, someone who does not have cavities probably won't even need to go and see a dentist.

Secondly, it doesn't follow necessarily that if psychiatry works, there would be less suicides in the treated population than the not-treated population. Recall that in the dentist example, people who haven't visited the dentist include those who do not have dental problems. In the same vein, people in the not-treated population include those who do not have mental health issues, and thus do not need to visit a doctor. On the other hand, those in the treated population include the severely suicidal, some of whom unfortunately cannot be saved. However, if, in a population of suicidal individuals, those who received psychiatric intervention had higher suicide rates than those who did not receive such intervention, this would be evidence that psychiatry doesn't help (or in this case, worsened things). Person 2 is committing the base rate fallacy.

Notice though, that you'd need to make comparisons between people who are suicidal, not between those that are suicidal and those who never sought any psychiatric help in the first place. The second category is much broader than the first.

I see non sequitur as well as a few unsupported and questionably true opinions in the exchange.

Person 2's "risk of suicide increases after consulting a psychiatrist" statement seems questionable in that it seems to be saying that consulting a psychiatrist makes suicidal people actually commit suicide.  It's not a claim I've ever heard before (and admittedly, I have no direct knowledge of the results from psychiatric visits for suicidal persons).  I find the claim hard to accept since it implies that psychiatric visits by suicidal persons are more "how to" sessions and less "treatment and prevention" sessions.  Possible, for sure, but it just seems odd and counter-intuitive, to me.

In the non sequitur department, we have the final exchange between Person 1 and Person 2.  Person 1 refers to "people going to the dentist" (presumably people looking for treatment for cavities); Person 2 responds by referring to "people who previously consulted a dentist" (presumably people engaged in longer-term dental care).  Certainly, there's an overlap of those two groups but the jump from one group to the other isn't a strong logical thread.

Person 2 then claims "(i)f psychiatry worked for suicidal people, there would be less suicides in the supposedly treated population than in those who never sought help from psychiatry."  This statement seems almost a tautology – aren't having a treatment work and having fewer people with the condition after treatment essentially the same thing?  

Also, I'm not sure what point either person is trying to make.  

Person 1 has a friend seeking psychiatric help for a condition and goes on to point our that people seeking psychiatric help for some condition are more likely to visit a psychiatrist than (presumably) persons without the condition.  The first statement is probably a statement of fact and the second seems pretty reasonable – but logically unrelated to Person 2's initial claim.

Person 2 makes an unsupported claim that seems intuitively false, to me.  Then, Person 2 goes on to propose a test for the effectiveness of psychiatry without offering any potential results from that test.

It seems to be a discussion in which both parties are talking past each other.