The human body is such a "perfect machine" it could not have naturally evolved. A particular creature or plant has such an unusual, perfectly-designed, unique system/set of skills/traits/etc. that there's no way this could have just happened. Theists have even been known to invoke Occam's Razor to claim that the most plausible explanation for uniquely special creatures is Intelligent Design.
Like many theological arguments, the Argument from improbability only works if one is intellectually dishonest or ignorant of the facts. When relaying this claim, theists always leave out a critical part of the process that nullifies the validity of the argument from improbability. Ironically, scientists agree, the likelihood of the human body being created "by chance" is ridiculously improbable, but that's not how evolution works. Creatures do not evolve "by chance" in some random nature as theists imply in this argument. Their environment forces them to adapt in specific ways or face extinction. This is called Natural selection. This is such an obvious, critical component of existence, which is observable by everyone, at almost any time, you have to wonder whether or not a theist using this argument is really that ignorant, or being intentionally misleading.
The human body is a most wondrous instrument. Isn't it amazing how we have so many processes going on that work so beautifully together? We have a built-in air conditioning system whereby we sweat to cool off, and an elaborate network of arteries and blood vessles; our brain is protected in a special "shell" and all our organs are tweaked to perfection to create a perfect machine. Atheists say we ended up this way evolving from monkey and lower life forms. Let me ask you something.. Can you imagine a hurricane blowing through a warehouse of parts and assembling a complete, working Boeing 747 airplane? This is what we're talking about in terms of the likelihood that the human body, an amazing machine, was created by chance. I don't think so. GODIDIT!
This is a spin on a lower level of the argument known as Hoyle's Fallacy:
The probability that a protein molecule could achieve a functional sequence of amino acids by chance alone -- Hoyle calculates this as being of approximately the same order of magnitude as the probability that a whirlwind would pass through an aircraft hangar full of airplane components and result in the assembly of a functional Jumbo Jet.
Ray Comfort demonstrates the Argument From Improbability
A classic example of the argument from improbability: Ray Comfort's infamous, Banana: The Atheist's Nightmare video clip. He also mixes this idea with the Argument From Design. It's so unlikely something so "perfect" was arbitrarily created, it somehow "proves" that it was "intelligently designed."
The ultimate irony of the Way of the Master video is that the banana Ray Comfort is holding was created by man. Naturally occurring bananas don't really look like that.
Evolution does not happen "by chance." Complex things are not arbitrarily created without rhyme or reason. This is the fatal flaw of the argument from improbability. It completely collapses the entire argument.
Natural selection is a documented, fact. It is a process by which creatures evolve through continuing to exist and better adapt to their environment through genetic mutation. This process is observable and provable, in addition to making a lot of sense.
Nobody disagrees with the claim that it's highly unlikely, for example, that a hurricane could blow through a warehouse and assemble an airplane. Apples and oranges. The development of complex life forms does not happen by chance.
Time is a major factor in the evolution of complex organisms. Technically it may be possible, that if you have enough monkeys banging on enough typewriters, for a long enough time, they may produce the complete works of Shakespeare. This sounds and is ridiculously improbable, but not impossible. However, imagine if each monkey who couldn't type was killed, and each monkey who demonstrated higher cognitive abilities pursuant to writing, was given a reward. You could in all likelihood dramatically increase the probability that monkeys would develop into creatures more capable of creating literary works. Multiply this over the course of millions of years and billions of generations of creatures and it does not look like a random thing. This is how natural selection works.
The so-called "perfect machine" is anything but perfect in the first place. In every example cited by theists as perfection or amazing examples of supernatural design, one can find flaws, mistakes, vestiges of obsolete functions or appendages. The human body is not a perfectly designed machine. It has many serious flaws that can only be explained by the process of evolution.
There are remnants of vestigial organs which don't seem to have a productive function any more: wisdom teeth, tailbone, etc.
Some organs and components are badly designed: the prostrate
The human eye and the way it interfaces to the brain is bizarrely designed; what the eye perceives is actually upside down and backwards, and our brain has to flip it back around.
If people don't get enough sunlight (or, specifically, ultraviolet light), they suffer from Vitamin D deficiency, but if they get too much, they suffer from skin cancer.
In order to have a large human brain as well as the ability to walk upright, the birth canal is much more complicated than those of other species, and the birth itself is a complicated and painful procedure.
Barely used nerves and muscles, such as the plantaris muscle of the foot, that are missing in part of the human population and are routinely harvested as spare parts if needed during operations. Another example is the muscles that move the ears, which some people can learn to control to a degree, but serve no purpose in any case.
The pointless existence of the appendix in humans, also the corresponding potentially fatal condition of appendicitis. The appendix, which is highly developed in herbivores, is meant to aid in the bacterial digestion of cellulose. Since people use fire and heat to cook now the appendix has become useless. (It has also been proposed that the appendix is involved in development of the immune system within the first year after birth, but subsequently has no function. However some people have congenital absence of their appendix without any reports of impaired immune system function.)
The route of the recurrent laryngeal nerve is such that it travels from the brain to the larynx by looping around the aortic arch. This same configuration holds true for many animals, in the case of the giraffe this results in about twenty feet of extra nerve.
The prevalence of congenital diseases and genetic disorders such as Huntington's Disease.
The common malformation of the human spinal column, leading to scoliosis, sciatica and congenital misalignment of the vertebrae.
The existence of the pharynx, a passage used for both ingestion and respiration, with the consequent drastic increase in the risk of choking.
The structure of humans' (as well as all mammals') eyes. The retina is 'inside out'. The nerves and blood vessels lie on the surface of the retina instead of behind it as is the case in many invertebrate species. This arrangement forces a number of complex adaptations and gives mammals a blind spot.
Crowded teeth and poor sinus drainage, as human faces are significantly flatter than those of other primates and humans share the same tooth set. This results in a number of problems, most notably with wisdom teeth.
Almost all animals and plants synthesize their own vitamin C, but humans cannot because the gene for this enzyme is defective (L-gulonolactone oxidase). Lack of vitamin C results in scurvy and eventually death. Defective vitamin synthesis pathways are a hallmark of "higher" animals — of which many are predators — because the prey accumulates vitamins that stems either from the eaten plants or are self-synthesized in the captured individual. Thus, higher animals are mostly unable to return to a purely "vegetarian" lifestyle; while conservation of such pathway genes is of no apparent cost to the animal.
The human reproductive system includes the following:
In the human female, a fertilized egg can implant into the fallopian tube, cervix or ovary rather than the uterus causing an ectopic pregnancy. The existence of a cavity between the ovary and the fallopian tube could indicate a flawed design in the female reproductive system. Prior to modern surgery, ectopic pregnancy invariably caused the deaths of both mother and baby. Even in modern times, in almost all cases, the pregnancy must be aborted to save the life of the mother.
In the human female, the birth canal passes through the pelvis. The prenatal skull will deform to a surprising extent. However, if the baby’s head is significantly larger than the pelvic opening, the baby cannot be born naturally. Prior to the development of modern surgery (caesarean section), such a complication would lead to the death of the mother, the baby or both. Other birthing complications such as breech birth are worsened by this position of the birth canal.
In the human male, testes develop initially within the abdomen. Later during gestation, they migrate through the abdominal wall into the scrotum. This causes two weak points in the abdominal wall where hernias can later form. Prior to modern surgical techniques, complications from hernias including intestinal blockage, gangrene, etc., usually resulted in death.
Other critics argue that if these design failures are the deliberate products of an intelligent designer, then the designer must be either inept or sadistic. Or possibly there was a large number of designers, as in the old joke that "a camel is a horse designed by a committee".