One of the favorite arguments that many creationists love to spout against evolution is the concept of "irreducible complexity." The argument is that living organisms have many organs that consist of many complex parts, and if you take any single part out, the organ becomes completely non-functional. Therefore it could not have formed on its own, because it would have required for all the hundreds of parts to have come together just in the right way at the same time.
This argument makes the same crucial (and rather stupid) mistake as those who argue against "half wings" and "half beaks." It assumes that organs formed fully developed, from its constituent parts.
There's a good analogy to demonstrate why this kind of thinking is nonsensical: A stone arc bridge. If you have an arc made of stones, if you take even one single stone away, the entire arc collapses. Therefore the arc is "irreducibly complex" by definition: You cannot take any single part of it away without the entire structure collapsing. What the fallacious argument would want us to believe is that, therefore, the arc was constructed by magic. (After all, it's impossible for all the stones to have been put all at the same time at their proper places; that's a physical impossibility.)
The mistake here is, of course, thinking that the stone arc was built by putting all the stones at their proper places, and that's it. It does not take into account that, in fact, it was built by using auxiliary support structures that were later removed.
This same phenomenon can perfectly well work in biology as well: Oftentimes some "supporting structures" (either literal, or functionally so) can become obsolete over time because the elements they are "supporting" become independent and can work on their own. Changes over time and natural selection can slowly make the obsolete part less and less important, until it completely disappears.
However, that's not the only mistake that the argument makes. An even larger mistake is to think that the constituent parts of an organ "come together" somehow ready-made. That's not how biology works. Organs change all the time over generations, in shape, size and functionality, even if so little. It's perfectly possible for a complex organ to form by transforming from one shape and function to another. It's not a case of ready-made parts coming together; it's a case of a structure changing into a different, more efficient form.
The eye is a perfect example of this, both because it's typically used as an example of "irreducible complexity," and because we know pretty well how the eye evolved during millions of generations. (The short version is: At first some skin cells were able to perceive light. It was then more advantageous if such cells were grouped close together. Then it was more advantageous if that area became concave because it allows perceiving light directionality better. Then it became basically a pinhole camera. And then the hole became covered by transparent tissue because it helped protect the whole. And then different shapes of the transparent tissue made vision better or worse, naturally selecting certain shapes over others. And so on.) And we actually have all of these stages in existing species, so it's not pure hypothesis. (It demonstrates that all these stages are, in fact, completely functional.)
This is a good example that it's not a case of "ready-made parts coming together" but rather an organ transforming over time. The end result may in some way be "irreducibly complex" technically speaking, but that doesn't mean that it couldn't have formed by slow transformation from one shape to another.