Final answer:
Fungal cell walls contain chitin and are supported by ergosterols, whereas plant cell walls are made of cellulose, demonstrating that they are not homologous. Fungi's heterotrophic nature and lack of photosynthetic ability further differentiate them from plants.
Step-by-step explanation:
The cell walls of fungal cells are not homologous with plant cell walls mainly because they are comprised of different materials. Fungal cell walls are primarily made of chitin, a tough polysaccharide also found in the exoskeletons of arthropods, such as insects and lobsters. In contrast, plant cell walls are made of cellulose, which is a different polysaccharide. Moreover, fungi are heterotrophic like animals, and do not have the chloroplasts necessary for photosynthesis, unlike plants which are autotrophs. Lastly, while fungi have plasma membranes stabilized by ergosterols, similar to cholesterol in animal cells, plants do not have this feature. Therefore, these differences in structure and function underscore why fungal and plant cell walls are not homologous.