The amount of genetic material passed on does not remain the same. Each offspring is an independent event, and which half of the genes gets passed along is selected randomly. So if an asexual organism has genes "A B C", then both it's two offspring will get "A B C". If a sexual organism has genes "Aa Bb Cc", and its first offspring inherits "A b C" from that parent, the second offspring could inherit "a b c" in which case the "B" allele is lost.

But that's not the argument they're making, the argument they're making is that the amount of passed genetic information is halved, because they fail to take into account that every offspring has two parents in sexual reproduction.

I've avoided doing so until now, but at this point I have to assume that you've only read the introductory paragraph of TFA and no further. The comment about only passing on half of an individual's genes is the author attempting (and not completely succeeding) to relate the well known, well studied costs of sexual reproduction to a lay audience.

This is not, however, what TFA is about. It is covering a course of research that is investigating whether or not sexual reproduction compensates for the difference in mutation rates between mitochondrial and nuclear DNA. You've managed to fill an entire thread with attacks on the introductory paragraph from a science journalist without once addressing the research being reported upon.

I did. If the premise of the research is invalid, the research itself must be invalid.

There is no such a cost of sexual reproduction. We need to separate sexual reproduction from having separate sexes. Hermaphrodite reproduction isn't very costly, the only cost is the cost of the sexual act itself.

Then, however, hermaphrodite reproduction is unstable, since it's obviously beneficial for the individual to only impregnate others, without prodicing eggs itself, and so passing the most expensive part of reproduction to others.

Then, the next question is why the females don't revert back to asexual reprodction, but 1. that has been observed in many species. 2. Purely asexual lineages tend to die out soon and 3. it's partially counterbalanced in many animals by the male providing some other benefit, like giving food to the female or taking care for the offspring.

While this is indeed somewhat paradoxical, it's in no way a mystery.

Another problem with this theory is that symbiosis and mutualism are not uncommon in nature. The way this problem is typically prevented (and it seems to be even a necessary condition for mutualism to remain stable, or even arise in the first place) is that there is some mechanism for culling or cutting off the symbionts that fail to provide the expected benefits. There is no reason to believe that the same isn't the case with mitochondria. Sex seems to be a very heavy handed way of doing so, and if it was so, you would expect people to die randomly without a clear reason when their mitochondria happen to mutate the wrong way.

And that recombiantion thing, that actually does happen, it's known as "outbreeding depression" and probably one of the reasons why species arise.