The formal name of the argument is the Teleological Argument. It is also known as “the argument from design,” or in trying to put a pseudo-scientific name on it recently, Intelligent Design. In modern times it is asserted as an alternative to Evolution by Natural Selection, and offered up for public schools as “teach the controversy.” (There is no controversy amongst scientists: the only controversy is those who seek to put religion in secular school science programs.)

It first appears in philosophy from Socrates, thus the argument has pagan roots. (If you need a quick debunk to a religious person, you can use that it is a pagan idea, not a Christian one.)

Though briefly flirted with by Islamic scholars in the Middle Ages, Islam rejected the idea as unnecessary to explain the Qur’an.

It was revived by St. Thomas Aquinas as the fifth of his “Five Ways” (proofs of God).

Protestant theologians picked up the idea in England and further advanced it. What became the fatal blow to the Teleological Argument was the 1859 publication of Charles Darwin’s “On the Origin of Species,” though Christians still continue to try and rehabilitate the idea (mostly by rebranding it: creationism, then Intelligent Design).

The first claim is that the universe appears ordered, so much so that it must have had a designer. That designer must be intelligent (as it is hard to imagine a designer that is not), therefore that designer must be more complex than the Universe. The only such designer proposed is gods. (In modern Christianity, the premise of Intelligent Design as pushed by its proponents tries to remove religion from the argument by not claiming what sort of designer is involved. That was notoriously shot down in the rial of Kitzmiler v Dover School District. The article at Wikipedia notes that Intelligent Design is indistinguishable from its creationist roots, previously shot down by the courts. It gives the fascinating breakdown of the proponents in court, when the school district was sued by parents for introducing Intelligent Design. The article also shows the dishonesty of the ID proponents in trying to smuggle in previously-banned creationism in their books on ID, especially “Of Pandas and People.”)

Arguments for Intelligent Design (ID) are mostly logical fallacies, particularly the Argument from Ignorance (I can’t think of anything better, so this seems good enough). Since creationists almost universally reject the Theory of Evolution by Natural Selection (because it stands in opposition to Genesis 1 and 2), ID proponents will try to use the Teleological Argument to “prove” that complex species, or even stars and galaxies are so complex they must be created. (That could be the case but exactly no evidence has been provided for that argument.)

One common argument used is the Watchmaker Argument (a watch is known to be created by humans, and watches are complex devices that do not arise naturally). Like most religious arguments, they are either borrowed from earlier religions or philosophies. The Watchmaker Argument is first noted by the Stoic philosopher Cicero:

• When you see a sundial or a water-clock, you see that it tells the time by design and not by chance. How then can you imagine that the universe as a whole is devoid of purpose and intelligence, when it embraces everything, including these artefacts themselves and their artificers?
• — Cicero, De Natura Deorum, ii. 34, (the nature of the gods), book II, XXIV

Cicero didn’t have two thousand years of scientific study to answer that question, so he can be excused.

ID proports to say that a complex object (such as an eye) needs all its components to function, therefore if even one component is missing (say a lens) the eye will not function. Therefore an eye could not have developed through natural selection (all the components would need to develop simultaneously, evolution is not a thinking process, therefore it could not predict an eye would even be needed or work.) This is a Black-or-White Fallacy (everything or nothing).

As it happens, an eye will function (poorly) without a lens. It functions with a malformed retina. It functions with a malformed cornea (for example, I’ve been told I suffer mild cataracts by an ophthalmologist, though I can see just fine). It even functions when the eye is misshapen (causing myopia, presbyopia, and/or astigmatism). In short you can still use your eyes, just not as well. (All those examples are why it’s a Black or White Fallacy—the presumption is if the eye has limited function or a missing or non-functional component, the eye can have no function.)

There are even single-celled organisms with a “patch” of sorts that can detect photons. That is pretty much the removal of every component of an eye except a rudimentary retina, yet that still gives the organism an advantage.

ID also presumes “order” must necessarily occur from a designer. Order is something that we perceive to make sense of the world around us. Frequently, ID proponents will try to throw out statistics (as in horribly bad odds) to claim that order one sees could not possibly occur by chance.

We have a universe, so the odds of at least one arising is of course unity. That proves nothing about a designer. It just proves we have a universe.

Another example would be a card game (I’ll use poker).
I could be dealt a hand of:
10♠, 9♠, 8♠, 7♠, 6♠

or I might be dealt a hand of:
K♠, 8♡, 6♣, 4♢, 2♣.

Both hands have precisely the same odds of being dealt. In poker, the first hand is a straight flush, and the second hand is something I would likely fold on the first bet.

However, the poker player (or even someone who doesn’t play cards at all) would likely see order in the first hand (the numbers are in sequence and all the same suit), and randomness in the second hand.

Another example is a variant of the Watchmaker Argument, the so-called “tornado in a junkyard” argument: The idea that a tornado cannot sweep through a junkyard and randomly assemble a jet aircraft, therefore evolution cannot be true. This of course completely misrepresents how evolution by natural selection works. It is intended to be used on people who do not understand evolution, and fails spectacularly when a person even has a cursory understanding of how evolution actually works.

The Teleological Argument in more modern times attempts to adopt scientific principles to uphold it as well, one of the common arguments being “if the nature of the laws of physics were altered even a tiny bit (for example, a change in the strong force), then life could not exist at all.”

This is another Argument from Ignorance (I can’t imagine a universe that might have altered physical properties, so one can’t exist).

It also makes the argument that the world (or the universe) must be designed, because the world is “just right” for people.

That ignores the point that the overwhelming majority of the world is inimical to the life of people (the oceans, the poles, high mountains, deserts, &c). The overwhelming majority of the universe is inimical to life at all (vacuum doesn’t really support life).

As you may notice going through each of these Apologetics Fails, the assertion made by a religious person is simple to do, but takes a lot of effort to refute. Moreover, if the assertion fails to impress you, the religious person will just move on to lower hanging fruit.