I'm yet to read evidence of HOW organisms went from asexual reproduction to sexual
Eden I don't have time right now - and you should be doing your own research anyway - but sex as we know it today did not happen all at once. (potential for double-entendre is exceptional in this thread).
I think you are asking about how rather than why. Here is a brief summary.
For 2 billion years life was prokaryotic - bacteria and archaea. They don't have sex but they do swap genes around very promiscuously.
Eukaryotic cells - the stuff oak trees, yeast, rabbits and humans are made of - arose as a result of a single event around 2 billion years ago when a bacteria that could produce energy using oxygen found itself prospering inside an archaea that couldn't. As a consequence of this event complexity became possible for reasons I'm not going to describe right now. The bacteria became the ancestor of the mitochondria that we have hundreds of in every cell producing energy through aerobic respiration. Sex began in these early eukaryotic cells.
The early stages of sexual reproduction did not involve internal fertilisation or external genitalia or porn videos. All of that took a long time to evolve. The road to proper sex - as opposed to lateral gene transfer - has to do with the relationship between mitochondria - who still retain some of their own ancient genome - and their hosts who hold most of the DNA in a nucleus.
There are three basic elements to sex. Not the ones you are probably thinking about right now.
1. Cell fusion
Mitochondria benefited from cell fusion which gave them new hosts in which to multiply. With the loss of the prokaryotic cell wall fusion was simple. Jumping genes that originated in the bacterial symbionts would likely be the driving force to induce cell fusion just as they are in some simple eukaryotes today.
Meiosis begins with the doubling up of chromosomes before dividing into four daughter cells. Mitosis, simple cell division, also begins with doubling up of chromosomes. Only one key change is necessary to convert mitosis into meiosis - a failure to digest all the cohesion proteins or "glue" holding the chromosomes together. This confuses the cell into thinking it is primed for the next round of chromosome segregation before it has completed the first round. Voila - gametes!
All the machinery required to recombination was already present in bacteria. The precise method of recombination is identical in bacteria and eukaryotes. Bacteria take up packets of genes all the time from their environment and incorporate them into their genome. In this way they can maintain small genomes and acquire other genes when needed.
Once endosymbiosis had occurred sex was not only mechanistically simple it was inevitable.
There is a lot more I could tell you - like why and how two sexes - but that will hopefully give you a hint that the authors of your article are dullards who have no interest in discovering answers to questions that seem to support their superstitions.
For more detail see "The Vital Question" by Nick Lane chapter 6 and "Life Ascending" chapter 5 by the same author.