My university professor stated that "individuals do not evolve, populations do". But aren't populations made up of individuals? That's like saying when a compound changes in stability, none of the elements' properties change. If someone could clear this up, that would be great.
individuals do not evolve, populations do is rooted in the (classical population genetic) definition of evolution. Here is this definition:
Evolution is a change of allele frequency through time in a population
Evolution is defined for a population, it is not defined for an individual. And it makes intuitive sense once you get more used to how evolution works. For example, the so-called fundamental principle of natural selection states that at any given time, the rate of increase in the population mean fitness is exactly equal to the variance in fitness.
Indeed, evolution is all about phenotypic and genetic variance (for fitness or other phenotypic traits) and without a population to observe, there is no variance. It is within this framework that people say
individuals do not evolve, populations do but you are correct that as populations evolve its constituents (the individuals) changes. The sentence has the advantage to reinforce the concept that evolution happens at the level of the population.
Evolution itself is a term that describes populations changing over time.
As Remi.b pointed out, if you take evolution to be genetic changes in a population over time, then it doesn't make sense for an individual to evolve. Evolution can only occur as genetic changes are inherited from parents to their offspring.
A given individual in a population can be subject to natural selection, but the individual itself cannot 'evolve' in the biological sense of the word. They can only contribute to the evolution of a population by affecting the allele frequencies in that population.
As an analogy,
The evolution of a population can be thought of as a motion picture of that population.
At any given moment, the genetic structure of a population can be thought of as a screenshot, and one person (or organism) can be thought of as a pixel.
Evolution is like watching a video of a population change through time.
So you might say:
"pixels do not play, videos do".
Evolution is about children differing from their parents. You are not identical to your parents.
- Your cells' DNA does change (a little, through new random mutations from time to time, most of it being repaired but not always correctly), but incoherently through cells, and these mutations are not transmissible if they are not happening in your gametes (sex cells).
- Non-lethal changes in your gametes are transmitted. Besides, errors in chromosome duplication is a way more efficient and fast way of evolving (mixing sentences makes sense more easily than mixing letters).