1. Everyone has problems
2. A rational person should should solve their problems in the most efficient way
3. Suicide is the most efficient way of solving all one's problems
4. From 1-3, a rational person should commit suicide
I shall justify these assumptions in turn and then follow up with some miscellaneous commentary.
Everyone has problems
If people have no problems, then the question immediately arises as to what they're actually doing if not solving problems. People avoid pain because pain is a problem and seek pleasure because the lack of pleasure is a problem. If pain were not a problem then people would be indifferent to pain and if the lack of pleasure was not a problem then they wouldn't bother seeking pleasure.
A rational person should should solve their problems in the most efficient way possible
All else equal, if there are two solutions to a problem and one is better than the other for whatever reason, then not choosing the better option is tantamount to indifference to the resolution to the problem i.e. the problem never existed in the first place. The only other case for someone knowingly choosing an inferior option and yet still believing in the problem is that the person is irrational.
Suicide is the most efficient way of solving all one's problems
The first issue to resolve here is whether or not becoming non existent would actually solve any of their problems. But solving a problem is equivalent to eliminating the problem for then the problem no longer exists and hence the problem is solved. Moreover, the same logic applied to all their problems shows that they are solved if they cease existing entirely.
On the question of efficiency, the quickest method of solving problems is to stop believing in them. For most people, this is quite difficult and in some cases impossible. The typical method of solving problems by directly undertaking some action that alters or effects a set of circumstances directly related to the problem is inefficient as it cannot guarantee that that problem and others won't continuously reoccur in future. Suicide solves all problems in one swing and is therefore better for those capable of carrying it out. It should be noted here that the practical details of the matter are not overly important to the argument but rather that suicide is the best way if only in principle.
It is my contention here that the human condition logically leads to rational self destruction. Of course, a person might be interested in solving problems of other people but self destruction is the ultimate goal even if that only occurs after everyone else has been destroyed. One significant remaining point is whether or not problems can exist even if people don't. For example, one might consider the absence of happy people in the universe to be a problem.
As a thought experiment, consider the idea that the number of grains of dust on the moon being prime is a problem. Clearly, this isn't a problem for any currently living people but who's to say that it's not a problem independently of people. If this isn't a problem in general, then for what reason? Perhaps we could create someone who believes a priori that the number of dust grains on the moon shouldn't be prime and thus that the whole moon should be vacuumed clean to preclude this possibility.
The question here is this: what distinguishes the two cases of the problem of there being no happy people and the problem of the number of dust grains on the moon being prime? Humans generally seem to regard the addition of happy people to the world a good thing just as the hypothetical person above regards the creation of new people to ensure that the continued dust equilibrium a good thing. However, if we move outside of these respective frameworks, we see that one thing is a problem if and only if everything else is because those things were only ever problematic for people inside those systems; outside the scenarios are indistinguishable. So if no one exists then either everything is a problem or nothing is a problem. Only the latter makes any kind of sense so it is most reasonable to conclude that problems necessitate people and thus that the destruction of all people can solve all problems.
There are clear allusions to antinatalism above even though the argument only intends to address rational self destruction. In particular, in upholding antinatalism, humanity would ultimately obtain a solution to all its problems. Thus instead of becoming a pleasure/pain antinatalist or similar one could become a problem antinatalist instead. A key difference in motivating antinatalism this way instead of pleasure/pain is that the problems in defending an asymmetry disappear under the alternative approach of solving problems because there is nothing to act as a counter point to solving problems. No one is interested in 'unsolving anti-problems' whatever that might mean. A natural asymmetry thus arises. The probable disadvantage lies in its abstractness which might make it unappealing for anyone who dislikes that approach. Another minor disadvantage is that most people are not fond of killing themselves no matter how ultimately rational that may be.