This was a first for me but I realized this is probably a common misunderstanding about genetics:
Let's unpack this a bit so we can see where this has gone wrong:
"Monogamy is biologically absurd", this must be news to the species that are largely monogamous and this person is clearly unaware of the costs of 'sperm competition' (if you are sleeping with lots of mates then, often, so are your competitors). There are also relationships between the vulnerability and cost of rearing young and the behaviors of parents of a species. Vulnerable and costly young tend to have long-term paired parents (probably no simple causation exists there, many factors are likely involved).
"To survive the species have to diversify their DNA", no, species tend to survive difficult events when they support a diverse population. That doesn't mean that species DO anything to ensure they diversify their DNA (indeed, most species have gone extinct). But the greater difficultly here is the implication that sexual promiscuity is a route to this genetic diversity.
It might sound plausible if you aren't aware of one extremely important aspect to our genetic diversity (which I wrote about previously), the process of DNA Recombination. This happens during meiosis (the special cellular replication process of gamete cells that produce ovum and spermatozoon) where allele's can get mixed between the parents chromosomes in prophase I when the homologous chromosomes pair up and trade small pieces of the chromatid. So the offspring are not stuck with merely getting a copy of either the fathers chromosome or the mothers chromosome, the chromosomes of the offspring is actually a unique mix of alleles from those between the two parents. This rapidly overwhelms any minuscule individual benefit as novel alleles spread through a population.
Let's also remember at this point that evolution doesn't take place within an Individual, it takes place in populations over time, with each step being dominated (in complex, multicellular sexual species) at the point of reproduction; so we need to consider long-term, population behaviors of genes. And between our meiotic processes and genetic recombination, sexual reproduction provides ample opportunity for novel genetic diversity rapidly spreading through populations regardless of the mating solution for a given species (which is dominated by asymmetric reproductive behavioral interests between the sexes).
Instead of number of mates, the impact of an individual on the future evolution of a population is largely determined by the number of SUCCESSFUL (keyword) offspring they have.
In the modern age, in a developed country, with ample resources, and an assumption that this will continue into the future (probably a bad assumption) then you *might* be able to argue that sleeping around could yield a greater number of surviving offspring than you could have in a purely monogamous arrangement -- but this could hardly have been selected for in the few short years we have enjoyed such circumstances (and the fact is, we see promiscuity used far more for pleasure than for reproduction). In the harsh, pre-enlightenment world that lasted 250K-100K years (just for anatomically modern humans, and millions of years for our primate ancestors) selection pressures yielded larger (and more costly) brains, and produced more vulnerable and costly young that required ever more sophisticated parentage to ensure success.
But I think our modern reproductive Monogamy was driven more by cultural pressures as societies grew in size and needed to manage things such as inheritance. But it certainly does not harm genetic diversity in a population.