The neo-Darwinian dogma that individuals do not evolve

Notoriously, evolutionary theory applies to populations. For evolution to operate, you need to have a population of variants for natural selection to choose between.

That evolutionary theory doesn't apply to individuals is enshrined in definitions of evolution, and is in textbooks (for example, Mark Ridley's "Evolution" textbook).

Here's Douglas Futuyma (1998):

The development, or ontogeny, of an individual organism is not considered evolution: individual organisms do not evolve.

Here's Larry Moran (2012):

Note that biological evolution refers to populations and not to individuals. In other words, populations evolve but individuals do not. This is a very important point. It distinguishes biological evolution from other forms of evolution in science (e.g., stellar evolution).

Here's Graham Bell (1997):

Individuals do not evolve; they develop, reproduce, and die. The characteristics of organisms, however, may change through time.

However, in universal Darwinism, individuals do evolve. Their brains evolve via learning. Their bodies evolve during development. Most Darwinian individuals are, in fact, populations on closer examination. Animals are populations of cells. Cells are populations of bacteria. Bacteria are populations of molecules. Molecules are populations of atoms - and so on. Many of those populations clearly evolve over time - event by completely standard evolutionary theory.

What are the neo-Darwinians thinking about? It isn't clear - but I think they are maybe trying to divide the evolutionary process up - so it only applies to one population (or level) at a time.

This seems silly. You can't have a system evolving from one perspective and not evolving from another one. Herbert Spencer's concept of a single unified evolutionary process is far superior. Here's Herbert Spencer (1862):

there are not several kinds of Evolution having certain traits in common, but one Evolution going on everywhere after the same manner.

Long ago, the idea that individuals were themselves composed of populations was not understood. It took a while to understand that these populations evolved by Darwinian mechanisms in a non-trivial way over individual lifespans. However, now this is understood. The idea that individuals do not evolve is outdated dogma. Dogma often takes a while to die - and this is a case in point.