It's not a system, it's the natural state of a lack of a system. It's what happens if you just let things play out without interfering at all.
Ultimately it's chemistry- the DNA is what reproduces in a highly dynamic system.

Suffering is a highly effective motivator for sentient biological robots, the robot that doesn't fear suffering doesn't fear having its DNA destroyed. DNA is an advanced kind of self replicating molecules, one produced from the suffering of less stable self reproducing molecules. Organisms in general are byproducts of DNA replication rather than the result of it. Organisms are shells, giant factories ultimately functioning to support the host self replicating molecules inside. Organisms are byproducts because it is not the only solution. Settle your brain into the pre-celluar stage of life where there were chemicals floating around in pools, self reproducing using the materials naturally available in the water and imagine if instead of fighting a cellular arms race between tank-factories (bacteria) and self replicating drone weapons (viruses and other simple replicators that lack the ability to replicate without hijacking the replication chemistry of tank-factories), the DNA could have formed a council and talked out their disputes, all agreeing to territory and limiting their populations, ultimately preventing the great arms race that led to today's diverse wildlife. Of course that's silly since DNA had no means to facilitate negotiations by themselves, but the point is that it's not so much competition as our human understanding of it portrays, but a natural process where DNA that does not reproduce does not reproduce, and the reasons that the DNA didn't reproduce have to fit in a naturalistic framework (IE no UN for proto-life chemical pools discussing alternatives to a cellular arms race and survival of the fittest).

And so the naturalistic framework extends to modern tank-creatures, giant japanese-style-combining-robots that combine billions of cell-tanks to produce a gargantuan. Each cell was like a small country with supply logistics, specialised workers, and now these cells themselves specialise inside a larger entity. What I'm leading to is that the cells created computational specialisation- the nervous system. Reacting to stimuli, moving around, and eventually self-awareness, all because they were more effective than the predecessors at having their DNA not not reproduce. Sorry for the double negative.

Suffering therefore is a computational strategy from the DNA to motivate the robot's self preservation, as DNA cannot directly arbitrate the actions of its creations, living almost as a captive of its own mad genius. Hardwire in something like tissue damage = suffering and you have basic behavioural patterns.

But can it be cruel? If DNA is ultimately responsible for all the suffering on earth, should it be put on trial?
Imagine if a computer scientist programmed a robot to feel pain, there would be ethical dilemmas- but from what I said earlier, ethics themselves are a creation of DNA to preserve itself. One thing I missed out is that DNA protects its information, not its physical structure. DNA that helps the reproduction of other copies of itself is more effective than DNA that does not, and so a result we have family ties, and racism, and all that discrimination based stuff.
Clearly, tissue damage to those more genetically similar to you (like family) is more compelling than tissue damage to others, which is the result of an ethics system, but an ethics system pre-programmed into you by the same DNA that causes people to suffer in the first place. How much can you trust it, really? How much can you trust you feelings on suffering knowing that they have been programmed into you by your genome?

Well here we lead onto another innovation of DNA: Dynamic computing- probably most easily understood as free will. It's not just thinking- because you can think about which limb to move next when walking but this doesn't require the kind of higher consciousness we actually have. Ultimately this is for strategic and tactical benefit. Foresight, the ability to dynamically solve problems and think about things. A kind of extremely generic computing (most of the brain is highly specialised, eg movement, heartbeat, speech, sense processing) was a new innovation, but allows us to think outside our genetic programming, and that is what you should be thankful for. It's not perfect since it's glued onto an ancient bed of superstitions and gut reactions, but it's all we have.
I'm really not sure where I'm going with this, sorry, but to link it into your post- darwinism is a system where lack of intervention is a necessity rather than an option.

One more thing I wanted to cover:
Competition. When humans picture competition they think of races, feats of strength and endurance, where effort is expended to the extreme to obtain victory. But competition between DNA is more like dropped two rocks into a pool of water. The one that hits the floor first wins, congrats. Not so much for the consequences but the process of competition- it's just natural processes. The water molecules bombard the rocks, slowing them down, but the rocks don't care. The rocks might not even have dropped at the same time. But differences between the rocks results in different outcomes.


You explain suicide the same way you'd explain anything else- darwinism isn't about godlike beings who are indestructible.
Like I said, DNA creates robots and pits them against each other. If you give your robot suffering as a motivation, and also give it volition, these interests are going to clash. To me it's explained by analogy: How come a cake tasted awful if it was a good recipe? Well the oven might have been awful. The ingredients might have been faulty. The cake might have been sabotaged by a rival cake. All the DNA can do is change the recipe and then hope it builds and runs correctly. I tried to portray DNA as a designer of automated robotics rather than a direct and ultimate control. Voiltion gives creatures a massive advantage, so they throw it in, since the losses to suicide and voluntary celibacy are a price worth paying for domination in other areas.

But I don't consider this the whole story- you could also make the argument that it's like how ants or bees behave. They're perfectly willing to sacrifice themselves for the greater good, although it's a little different since they cannot reproduce. But the point is that the suicidal ant and the hive share DNA so it is in the interests of the DNA to preserve the DNA of its peers. Still, with humans this makes much less sense, since the proposition that a human eats less resources (by dying or not reproducing) that its peers could use falls since children would share more DNA than anyone else, except identical twins.

So really it's some kind of programming error- but the programming isn't done sentiently, it's done chaotically, so while suicide is likely a bug in the software, the code that has the bug in is so useful that fixing the bug would reduce the effectiveness of the code. I could almost say that the bug was intentional since it's not really a bug but a choice- the choice to have extreme emotional capacity for extreme motivation, weighed against the extra risk of the extreme emotions causing self termination. Or in voluntary celibacy, the high capacity for independent thought and the high control over behaviour gives a massive advantage in coordination and tactics but sometimes results in people not reproducing when it perhaps clashes with some other programming.

It's a tradeoff made in the chaotic nature of the programming itself, iterative and chaotic.
'For the greater good' arguments might explain some suicides like jumping on a grenade, but it can't explain someone falling into a pit of despair and then putting a gun to their head. To me, the brain is programmed in a 'This code works and I have no idea why' kind of way. Like a mess of cables- visualised in my pictures- just like what you think when you see the shit on the left. And the neat one on the right(?) being absolutely not what it's like at all. The clean one was put in all at once, but the messy one was done iteratively, with patches, additions and 'eh it works' attitude.