Sexual reproduction fosters greater genetic diversity in the population. Asexual reproduction tends to be cloning with a lot less diversity. Greater genetic diversity means there's less likelihood that all members of the population would die out in a disease outbreak; less likelihood that all animals would lack the traits needed to survive if the environment changed. So genetic diversity provides a survival and therefore a reproductive advantage to species. Natural selection selects those species for survival while those who reproduce only asexually are prone to dying out unless they have some other survival advantage that counterbalances their disadvantage.
A good way to illustrate this is to think of a diversified economy verses an economy based on one or very few productive sectors. The diversified economy is more robust because if a disaster affects one sector it only affects a small percentage of the economy. But an economy based on only one productive sector is destroyed if that one sector is affected by a disaster.
I don't trust what intelligent design advocates have to say about evolution. They always see problems with evolution based on their prior commitment to creationism; their use of fallacious thinking; selective, out of context quotes and outright lies and deceptions. Watchtower does not have a monopoly when it comes to distorting the facts about evolution.
I skimmed through the article. Nothing about it jumps out at me and says: "aha! sexual reproduction could not have come about without an intelligent designer". Instead the whole article is nothing more than the tired old argument from ignorance fallacy. Not yet having a natural explanation for some biological phenomenon does not mean one will never be found in future and it does not mean that a convoluted explanation involving a magic man in the sky automatically becomes the most viable explanation. One thing that did strike me about the article is the fact that it quotes old sources. Look at the dates of the sources in the end-notes at the end of the article. They're mostly from the 1970's to the 1990's. This leads me to ask the question: what are scientists today, in 2016, saying about the "problem" of explaining the origin of sexual reproduction.