I can see a couple of problems with your basic assumptions.
1) there must be a genetic mutation in the gene pool. (rare)
Mutation rate is one mutation per 50 million bp/organism. Each human is carrying over 100 mutations. I'm not sure how that counts as "rare"
2) this mutation must be beneficial. (very rare. As a matter of fact, we've never seen it happen, and if we have, then why don't evolutionists show us beneficial mutations instead of nonbeneficial ones?)Beneficial mutations are well known, if you haven't heard of any then you haven't looked. Apo-A1 Milano made quite a bit of news. Nor does a mutation have to be immediately benefical, neutral mutations do quite well.
A recent study showed that only 36% of point mutations rendered a protein non-functional, so that means that over 60% of mutations are non-deleterious
Every other point beyond this is a strawman.
Reproduction is a continuum, not a boundary.
The earliest organisms capable of sexual reproduction would also be capable of asexual reproduction, such as is seen today amongst the algaes. Nor would "male" and "female" be a requirement... just two haploid cells.
The cells of most sexually reproducing animals contain two sets of genes, asexually reproducing creatures carry only one set. That means that the proto-sexual reproduction was a matter of two organisms combining, or a polyploidy. But these early fusions didn't have to be sexually reproducing, they could go along merrily asexually reproducing their diploid selves forever. With diploid genes in place, the only thing you need is meiosis, an error in cell division. If this is an environmental trigger (as it is in certain algaes) then many of these creatures would produce haploid cells at the same time, thus increasing the chances of finding another haploid. If they didn't? Then they are still capable of reproducing asexually.
Being as we have such organisms with us today, why would the earliest sexual reproduction have to be more complicated ans developed?
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