writersoul,
How do you know the chicken statistic isn’t true? Not because you’ve done a scientific study and produced contrary statistics, but rather because there is overwhelming anecdotal evidence to the contrary.
In the case of the shidduch crisis, there is overwhelming anecdotal evidence that girls have a harder time getting dates than boys. A statistical study would be useful to know exactly what the ratios are and it might help us determine the cause of the discrepancy but we don’t need statistics to know there is a problem.
Health,
This has all probably been discussed before but the S”A does not require a woman to get married. It only requires a man to get married. Second, Even HaEzer 2:9 expressly states that a young man should not marry an old woman and an old man should not marry a young woman. See also Yevamos 106b the mishna and the first Rashi on the page.