To be more specific: the light isn't stretched because the two objects are getting farther away from each other in the conventional sense. If than kind of movement generated redshift you'd see it all the time, in the light from passing cars, or stationary lights as you speed by them. Redshift is caused by
space itself expanding as the light travels through it. This stretches the light, lowering its frequency. If we could observe matter travelling at or near the speed of light in expanding space, we'd see the matter itself being stretched.
Of course, all of that is hypothesis, and rather bold at that. Scientists observed redshift, and decided that the only sound explanation was that the space was expanding. The Big Bang theory already existed at this point, and that was one of the reasons the space-expansion hypothesis was supported: it fit nicely into Big Bang cosmology. But the Big Bang theory doesn't really need redshift.
Constable Jaynin Mimetes wrote:
There's a book out there called "The Big Bang Never Happened" by Eric Lerner. I haven't read the book yet. I resisted it because, as I kept telling my dad, I believe in the big bang! The alternative is a steady-state universe, which is silly. However, Eric Lerner's argument for a steady-state universe is that redshift as a method for measuring the distance of galaxies is wrong. And his source material is research by a well known Canadian astronomer - Halton Arp.
I agree that the steady-state universe is silly. However, there are other alternatives than the Big Bang theory. The Big Bang model is simply the most popular, primarily because (as I like to remind young-earth creationist) it absolutely
requires, in any model, millions of years to even evolve stars, let alone planets, let alone stars and planets of the apparent age and variety which we observe in the larger universe. There has been, as yet, no scientifically viable framework in which the Big Bang can be made to fit the Young Earth timeline. Additionally, the Big Bang contradicts the literal reading of the order of creation events in Genesis. This also happens to be why I reject the Big Bang theory, although that's beside the point, as I'm not trying to argue with you, but instead to point out alternative cosmologies which offer other explanations for redshift.
For example, Dr. Russel Humphreys has proposed that all matter in the universe was created compressed within a block hole. But immediately after creation, the black hole transformed into a "white hole". In a white hole, no matter can pass within the event horizon. This means all the matter within can escape. As the singularity looses mass, the event horizon collapses, forcing more matter out. The theory also assumes that the universe has a fixed boundary, whereas the Big Bang model assumes that the universe is infinite and continues in every direction, containing an infinite amount of matter and energy.
It's significantly more complex than that. But the end result is that only a brief amount of time passes at the center of the universe, where the objects in our solar system coalesced more quickly because of various unique properties. But farther and farther away from us, time has passed at an increasing rapid rate. At the very edge of the universe time has gone on for thousands of years (this also has the virtue of explaining distant starlight in the young earth timeframe). Anyway, because of the gravitational waves that would linger due to the black hole and the white hole, light is redshifted as it travels towards us from distant objects.
Another theory I have seen, though I can't speak to its scientific accuracy, assumes that the universe has a center which we are very near to, and that as a result, light traveling towards us is stretched. If you imagine a light wave or beam of photons traveling towards the center, the photons or waves towards the front would be experience slightly greater gravitational pull. This would stretch the light, decreasing the frequency, causing redshift. Of course, this theory would imply that light doesn't travel at a fixed rate, but Einstein himself pointed out that there is no direct evidence for a fixed rate of light travel.
There is also the theory that the speed of light itself is decaying, and thus stretching the light as a decelerates. I see two main problems. First of all, since redshift is uniform, this means that the speed of light has been decaying at a uniform rate everywhere and for all time. Secondly, since redshift is a real-time, observable phenomenon, that would mean that lightspeed is decaying at a rapid, observable rate. If that were true, we'd be able to record the decay in progressive lab tests. But the speed of light in a vacuum hasn't observably changed for as long as we've been able to obverse it.
I'm certain that there are other theories. I think the Electric Universe model has some explanations.