I guess that most of us have a family tree, and even if we did not make it ourselves, there is surely a relative in the family that spent considerable time (hundreds, if not thousands of hours) researching in archive rooms to go back as far as possible in time. There is often some kind of pride in some families to be able to claim that one descends from this or that famous ancestor who lived hundreds of years ago. Many will claim royal ancestry, and that typically ends up with the oldest surviving family trees in Europe, like those of the Carolingian and Merovingian dynasties. In fact, in countries where paper trails are particularly good, like in the UK, with a bit of effort almost anyone can find that they descend from Charlemagne and Clovis. Even if they can't, chances are that they do descend from them anyway, like most of us.
This in itself is not very bothering. Humans have sought to self-congratulate themselves and to seek pride in intangible and meaningless things like one's belief in an invented deity, or some potential descent from a medieval monarch about whom they usually don't know much really.
I was startled and rather disturbed to find out that the majority of people who order DNA tests do it for genealogical purposes, e.g. to complete their family tree or find distant cousins. I think that it's rather moronic (and I don't remember when is the last time I had to use that word before). I am going to justify myself, because obviously I cannot just say that something (or someone) is moronic without explaining why.
1) There is no point in claiming descent from ancestors who lived more than two centuries ago, because you may not have inherited any DNA from them
I suppose that part of the problem is that most people are inherently bad at maths. We inherited
approximately 50% of our DNA from each parent, but because of DNA recombination we do not normally get just 25% from each grand-parent. It can be 23.642% or 26.87236% or whatever, but exactly 25% is almost unheard of. Therefor we do inherited more from some grand-parents than from others. This phenomenon amplifies at each additional generation. We may inherited about 18% of DNA from one great-grand-mother, but only 9% from another one. That's a two-to-one ratio, and only after three generations. Forget about text books that ridiculously explain that we inherit a fixed 12.5% from each great-grand-parent. That is misleading at best, especially when we apply the same logic to more distant generations.
After 7 generations, we do not inevitably inherited a mathematical 0.78125% of each ancestor's genome but that some ancestors contribute to more than 2% and others to 0%. And that's barely after 7 generations. People who pride themselves in descending from Charlemagne do not seem to understand that the man lived over 40 generations from us. In other words, even if his genetic contribution was not eliminated by recombinaisons somewhere along those 40 generations, the amount contributed would be less than 0.0000000001% of the genome.
All this to say that single ancestors on a family tree do not contribute anything meaningful to one's genome after a few generations. The only ancestor that keeps contributing the same 1% of DNA generation after generation, even after 1000 or 2000 years if the one on the patrilineal line for men. But what does that mean to share a Y chromosome? I have several paternal uncles and cousins sharing my Y chromosome and they couldn't be more different from me in every regard. We literally don't share anything in common.
2) Third and more distant cousins do not share any meaningful amount of DNA with you
Through of the laws of genetic recombination, siblings statistically share 50% of their genome, but in practice may share very different percentages, maybe between 40 and 60%. So your sibling's children may inherit about 20 to 30% of your DNA. According to
23andMe (based on observed customer data), first cousins share 7.31% - 13.8%, 2nd cousins 2.85% - 5.04%, and 3rd cousins a paltry 0.2% - 2%. In other words two men who share the same Y-chromosome, but separate by dozens of generations and with no known genealogical ties, may share more DNA through their Y-chromosome alone than two proven third cousins. That's just the way it is. Third cousins are not better than strangers in terms of genetic similarity. Anybody who believes that they are finding "blood relatives" when finding third or fourth cousins through DNA testing companies are badly deluded.
Even if they were to find first or second cousins that they didn't know about (I wonder how that's possible unless one was adopted), that still wouldn't guarantee that you share anything in common, be it for tastes, sensitivities, interests, way of thinking or whatever else matters in a relationship with another human being. If you are looking for people like you, join interest groups or online forums like this one. Don't waste your time imagining that because you share a few percent of DNA you will be compatible in any way. Just look at the number of siblings who can't stand each others, or at least don't have anything in common.
Conclusion
Attaching importance to distant ancestors or distant cousins in one's genealogy is almost as irrational and meaningless as astrology. People purchasing DNA tests for that sole purpose are wasting their money.
It's very sad because DNA test are so revolutionary and fantastic in so many ways. Everybody should have their genome sequenced, if only to know about their health risk. I absolutely cannot understand why anybody would not want to know who they are, or fear to find about disease risks (the logic is that if you don't know you can't prevent it and therefore you are likely to die from it). Why are people wasting their time with genetic genealogy and finding distant relatives?
For anybody interested in (pre)history and/or anthropology (e.g. human variations across ethnic groups, but also variations in time, across historical periods), DNA tests are a total boon. We could never hope for such a wonderful tool to solve many of history's secrets. It's ironic that Europeans, who care much more about history than almost anyone else, order less DNA tests than Americans. It's even more ironic that among Europeans the French may be the most obsessed about history, and yet it is the only country in he world where DNA tests are prohibited by law (what terrible secrets may they be hiding?).
