This will be as brief and as simplistic as possible for obvious reasons.
Humans share approximately 98.5% of their DNA with chimpanzees. So, for this example we will need to temporarily accept the premise that DNA can be mutated (changed) by at least 1.5%. The problem is that mutations are entirely random meaning that a mechanism potentially capable of mutating ~1.5% of a chimpanzee’s DNA to exactly match human DNA could also mutate it 1.1% or 0.45% or 0.37940%, or 1.20238943029423%, or 1.49% or 1.499% or 1.4999% or 1.49999%, or 1.499999%, or 1.4999999%, or 1.49999999%, or 1.49999999999999999999999999999999999999999999999999999999999999999999…%, etc., ad infinitum, and in a virtually infinite number of “directions.” (This is known as an infinite series in calculus.) And, since there are only a finite number of specific genetic codes which could produce a human, to quote Douglas Adams, “any finite number divided by infinity is as close to nothing as makes no odds…” (And, that’s without mentioning that 98.5% is an average, meaning that slightly more or less DNA can be shared between certain individuals of both species.)
In other words, you have a much better chance of landing a baseball in a specific six inch spot on Pluto (still not a planet) by launching it in any direction from Earth at random. If you are incapable of grasping just how ludicrous this is, consider that (1) Pluto is on average 40 times farther away from the Earth (~3.7 billion miles) than the Earth is from the Sun (93 million miles), that (2) ~50% of the directions you could launch the ball in would result in it hitting the ground on Earth, that (3) Pluto is very small, about a third smaller than our Moon, (a walk around Pluto’s equator is much shorter than a walk across Russia) that (4) the ball would be affected by the gravity of every mass in the solar system, etc., etc. I could go on and on, but you should get the point by now.
So, that’s why a chimpanzee cannot give birth to a human. Now, on to why a chimpanzee being unable to give birth to a human does not disprove evolution…
Ironically (and unsurprisingly), creationists have this issue entirely backwards: they believe that evolution is false because a chimpanzee has never given birth to a human. In reality, the fact that a chimpanzee hasn’t given birth to a human is evidence for evolution. If a chimpanzee did somehow naturally give birth to a human, it wouldn’t “prove evolution” as creationists are wont to say: it would disprove evolution! Why you ask?
Well, evolution as we understand it* occurs gradually over a long period of time. Apes (ape-like animals) didn’t just magically become humans, nor did feathered dinosaurs magically become modern birds: over a very long period of time (hundreds of thousands and millions of years) they gradually became something else and then something else and then something else, etc., and in hundreds of thousands and millions more years they’ll be something else entirely again (or extinct). Think of it like you think of time:
Imagine two scenarios: (1) you observe an analog clock for an entire hour specifically observing the movement of the hour hand, and (2) you observe the clock at a specific starting point, set an alarm for one hour, and when the alarm buzzes you observe where the hour hand currently is and compare it to where it was at the specific starting point.
Scenario 1: If you stare at an analog clock for an hour, say from 3:00 PM to 4:00 PM, you observe that the hour hand slowly (gradually) moves from 3:00 towards 4:00 rather than jumping straight from 3:00 to 4:00. This is how evolution “works:” a species can gradually change into something else entirely just as our hypothetical clock gradually changed from 3:00 to 4:00, except that in this case, the time it takes to get from 3:00 to 4:00 is anywhere from hundreds of years to millions of years rather than one hour (depending on the species). This means that apes did not give birth to humans, as every species can only give birth to offspring very much like itself; however, since you’ve already accepted the fact that offspring are not perfect replicas (similar but inexact), you can see how over a very long period of time, say a few hundred thousand years of inexact replicas giving birth to inexact replicas giving birth to inexact replicas giving birth to inexact replicas, etc., how you can end up with something entirely different than that with which you began. That description of the process of evolution is about as nontechnical as one can get.
Scenario 2: Interestingly, however, if you observe the clock at 3:00 PM and then set an alarm to go off exactly one hour later at 4:00 PM, and you do not observe the clock again until after the alarm buzzes, the clock will have appeared to have jumped straight from 3:00 to 4:00. This is how your mind processes the phrase “humans evolved from ‘apes'” if you have no understanding of evolution. Just as you observe the clock at 3:00, then the alarm buzzes an hour later and it appears to have jumped to 4:00, you believe apes (3:00) turned into humans (4:00) without any intermediary steps. In reality, an ape-like species gradually became many different species over millions of years on the road to becoming us, just as 3:00 gradually became 4:00. It’s like being given a picture of a person at age 5, then a picture of them at 70: since you understand the human aging process since you go through it yourself and have seen many others go through it, you don’t think, “Wow, that person was 5 a minute ago and now they are 70! What gives!?” No, you know that this person lived out every second, minute, hour, day, month, year, etc., of their lives from age 5 to age 70, just as an ape-like ancestor of ours gradually became something different, then something more different, then something even more different, etc., over tens of thousands to hundreds of thousands to millions of years. The real problem, then, is that it’s not common sense, and the time scale is far greater than you or I can imagine. (Food for thought: would aging make sense if you fell into a coma at age 5 and woke up at age 70?)
So, Scenario 1 can be thought of as a metaphor for “microevolution,” whilst Scenario 2 can be thought of as a metaphor for “macroevolution.” They are not exact metaphors of either, but they are similar. What’s important to note here, however, is that microevolution and macroevolution describe exactly the same processes (evolution!), but they do it using different timescales: macroevolution is basically the result of microevolution over a very long time. I’ll go into this in greater detail on this in the near future!
In conclusion, we’ve shown that the odds of a chimpanzee giving birth to a human are infinity to one, and that this fact does not disprove evolution. Rather, it shows that species cannot give birth to other species out of the blue, but that species gradually evolve into other species over a very long period of time. If you’re still having trouble with this concept, write in the comments below, and I’ll be sure to get to your comment as soon as I can.
*Do not take the phrase “as we understand it” to mean that there is some other possible explanation we don’t understand. For example, “as we understand” gravity, it’s that a mass is attracted to any other mass by a force. More specifically, any mass (say, Earth) is attracted to any other mass (say, Jupiter) by a force directly proportional to the product of their masses and inversely proportional to the square of their distances.