why is it so important to use a large number of fertilizations and off sring when studying mendelian genetics?

Answer 1

Small sample sizes can introduce errors in results. Each reproductive event has the same chances as any other but sometimes events repeat. In a large number these small clusters of like events average out.
If you flip a coin three times and only get heads you would not be representing the same ratio of results as the next three dozen flips.
Large numbers can also show if there are other factors than random chance influencing the results that may not be obvious in small data sets. It is possible to design an experiment with unaccounted variable that can skew the expected results. Mendelian genetics only works when the traits assort independently. With linkage and crossover large sample numbers show this phenomena.