Because cats and birds long ago came, unwittingly, to a mutual accommodation in which both can survive. If birds could breed unchecked, there would soon be far too many birds for their food supply to support them. A female starling, for instance, lays about 16 eggs in her life. If they all survived, and this continued, the starling population would multiply by eight every generation, 16 babies for every two parents. Such 'exponential' growth is amazingly rapid: by the 70th generation a sphere the size of the solar system would be occupied entirely by starlings (instead of by pigeons, which appears to be its natural destiny).
The only 'growth rate' for the population that works is for each breeding pair of adult starlings to produce, on average, exactly one breeding pair of adult starlings. Replacement, but no more, and no less. Anything more than replacement, and the population explodes; anything less, and it eventually dies out. So of those 16 eggs, an average of 14 must not survive to breed. And that's where the cat comes in, along with all the other things that make it tough to be a bird, especially a young one. In a way, the cats are doing the birds a favour, collectively, though maybe not as individuals. (It depends if you're one of the two that survive to breed or the 14 that don't.)
Rather more obviously, the birds are doing the cats a favour, cat food literally drops out of the skies, manna from heaven. So what stops it getting out of hand is that if a group of greedy cats happens to evolve somewhere, they rapidly eat themselves out of existence again. The more restrained cats next door survive to breed, and quickly take over the vacated territory. So those cats that eat just enough birds to maintain their food supply will win a competition against the greedy cats. Cats and birds aren't competing because they're not playing the same game. The real competitions are between cats and other cats, and between birds and other birds. This may seem a wasteful process, but it isn't. A female starling has no trouble laying her 16 eggs. Life is reproductive, it makes reasonably close, though not exact, copies of itself, in quantity, and 'cheaply'. Evolution can easily 'try out' many different possibilities, and discard those that don't work. And that's an astonishingly effective way to home in on what does work.
As Huxley said, it's such an obvious idea. It caused so much trouble from religionists because it takes the gloss off one of their favourite arguments, the argument from design. Living creatures seem so perfectly put together that surely they must have been designed, and if so, there must have been a Designer. Darwinism made it clear that a process of random, purposeless variation trimmed by self-induced selection can achieve equally impressive results, so there can be the semblance of design without any Designer.
There are plenty of details to Darwinism that still aren't understood, as with all science, but most of the obvious ways of trying to shoot it down have been answered effectively. The classic example -still routinely trotted out by creationists and others even though Darwin himself had a pretty good answer, is the evolution of the eye. The human eye is a complex structure, and all of its components have to fit together to a high degree of accuracy, or it won't work. If we claim that such a complex structure has evolved, we must accept that it evolved gradually. It can't all have come into being at once. But if so, then at every stage along the evolutionary track the still-evolving proto-eye must offer some kind of survival advantage to the creature that possesses it. How can this happen? The question is often asked in the form 'What use is half an eye?', to which you are expected to conclude 'nothing', followed by a rapid conversion to some religion or other. 'Nothing' is a reasonable answer, but to the wrong question. There are lots of ways to get to an eye gradually that do not require it to be assembled piece by piece like a jigsaw puzzle. Evolution does not build creatures piece by piece like the God of Evolution in The Last Continent. Darwin himself pointed out that in creatures alive in his day you could find all kinds of light-sensitive organs, starting with patches of skin, then increasing in complexity, light-gathering power, and ability to detect fine detail, right up to structures as sophisticated as the human eye. There is a continuum of eyelike organs in the living world, and every creature gains an advantage by having its own type of light-sensing device, in comparison to similar creatures that have a slightly less effective device of a similar kind.
In 1994 Daniel Nilsson and Susanne Pelger used a computer to see what would happen to a mathematical model of a light-sensing surface if it was allowed to change in small, random, biologically feasible ways, with only those changes that improved its sensitivity to light being retained. They found that within 400,000 generations, an evolutionary blink of an eye, that flat surface gradually changed into a recognizable eye, complete with a lens. The lens even bent light differently in different places, just like our eye and unlike normal spectacle lenses. At every tiny step along the way, a creature with the improved 'eye' would be better than those with the old version.
At no stage was there ever 'half an eye'. There were just light-sensing things that got better at it.
Since the 1950s, we have been in possession of a new and central piece of the evolutionary jigsaw, one that Darwin would have given his right arm to know about. This is the physical, more precisely, chemical, nature of whatever it is that ensures that characteristics of organisms can change and be passed from one generation to the next.
You know the word: gene.
You know the molecule: DNA.
You even know how it works: DNA carries the genetic code, a kind of chemical 'blueprint' for an organism.
And, probably, a lot of what you know is lies-to-children.
Just as 'survival of the fittest' captured the imaginations of the Victorians, so 'DNA' has captured the imaginations of today's public. However, imaginations thrive best if they are left free to roam: they grow tired and feeble in captivity. Captive imaginations do breed quite effectively, because they are protected from the terrible predator known as Thought.
DNA has two striking properties, which play a significant role in the complex chemistry of life: it can encode information, and that information can be copied. (Other molecules process the DNA information, for example by making proteins according to recipes encoded in DNA.) From this point of view a living organism is a kind of molecular computer. Of course there's much more to life than that, but DNA is central to any discussion of life on Earth. DNA is life's most important molecular-level 'space elevator', a platform from which life can launch itself into higher realms.
The complexity of living creatures arises not because they are made from some special kind of matter- the now-discredited 'vitalist' theory, but because their matter is organized in an exceedingly intricate fashion. DNA does a lot of the routine 'bookkeeping' that keeps living creatures organized. Every cell of (nearly) every living organism contains its 'genome', a kind of code message written in DNA, which gives that organism a lot of hints about how to behave at the molecular level. (Exceptions are various viruses, on the boundary between life and non-life, which use a slightly different code.)