Why is fertility measured by number of children women have and only seldom by the number men have?

There is no theoretical reason for giving priority to women’s fertility. The main reason is that the information available on father’s identity when the birth is registered is of lower quality than for women. The paternal filiation of children born outside marriage is harder to establish with certainty and may be inaccurate, whereas the filial tie between a newborn and the woman who has given birth to that baby is obvious. Moreover, study of retrospective surveys on past births reveals that men tend to underreport the number of children they have had.

Additionally, the fact that the reproductive period of women’s lives is shorter than that of men confers a methodological advantage on measuring women’s fertility: the completed fertility rate for a given generation of women can be determined earlier than for men—no later than age 50. Lastly, demographers continue to prefer the female fertility index  for comparison purposes as it is used in all countries—and despite the fact that data on men are also reliable. (It should be noted that INSEE is now correcting for missing information on men’s ages at paternity.)  

The fact is that measuring women’s fertility rather than men’s is not a neutral choice because men and women do not have the same number of children.