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Genetics is a relatively new and broad field. It can be roughly divided into four major areas. There are topics within each of these subfields that every biology student should be familiar with.
Teaching topics like recombinant mapping, population genetics, heritability, and epistasis is not as directly important to the modern general practice of genetics. However, it is valuable in that it shows the power of logic and inference to use observations to construct models of how the system works beyond the immediately observable surface of things. Geneticists used logical inference to map out biochemical pathways, map genes onto chromosomes, determine that behaviors were composed of both genetic and non-genetic influences, and infer natural selection acting upon genetic variants, long before it was possible to study these processes at a molecular DNA sequence variant level. The demonstrated power of logic, observation, inference, and model building is a valuable lesson to anyone working in any field.
There are also important topics that touch on social issues related to genetics that should be included in a biology education.