Perhaps there is some agenda here that I'm missing. Is the point that octopus should not be kept by amature aquarists? Or is it that people should not try to breed them? Or is it that the life history of octopus is solitary, poor, nasty, brutish and short (can't remember is I got that quote right)?
Much of what was suggested is correct, but the fact is, it is not at all difficult to mate octopuses and it is not that hard to rear juveniles. It all comes down, as usual, to what species you are dealing with.
Sexing octopus is not always that hard, but you have to know the species and what you are looking for. In some species such as O. wolfi it is really easy, in others it takes practice. The fact is that if you look at the hectocotylus carefully, there will usually be morphological characters that are easily seen - although you may need a magnifying glass if you have eyes like mine.
Most octopus are opportunistic breeders and will mate whenever an adult male meets an adult female. A sexually mature male will often try to mate with any other octopus that even vaguely fits the bill - male, female, even a member of another species. You simply have to put them together and wait for an interaction, then remove the male after mating. Yes, females will occsaionally attack and eat males, but that is rare in most species. I've mated lots of pygmies and have only had it happen twice, both times in H. lunulata and only after the male had successfully passed several spermatophores.
Yes, males of all species will die, but how that relates to sexual activity is largely unknown. They certainly do not drop dead after mating once with a female. We can often use a male as a stud for weeks.
Brooding females are secretive, but most survive until after the eggs hatch and the paralarvae leave. That's octopus life. Apparently some people find this tragic, other noble, and others "that's the way selection shaped it". There are lots of animals that reproduce just once including some mammals. That just happens to be what has worked for this species..
Yes, small egg species produce paralarvae that are almost impossible to rear in a home aquarium, but big-egg species produce "crawl away" larvae that begin feeding immediately on small prey such as amphipods and they are relatively easy to rear. You have to know what you are doing, but it is not rocket science There is plenty of information available on this and other websites that can guide you.
If you know the basics of keeping a healthy aquarium and have been able to hold an octpus for at least a few months, there is no reason you should not move on to the next step of trying to breed them
Roy