Breaking down the question on personality by fertility lends credence to this assertion. The first kid forces parents to come to the realization that the way little Hayden turns out is not something they have complete control over (if much at all). Subsequent children show, through countless contrasts with their other siblings, that from the same nest very different rugrats scurry forth. The following table shows how fertility influences perceptions in this area. The percentage of women who believe genes play a primary role in determining personality by number of children (N = 1222):
While it's easier to hold quixotic notions of human nature in youth than it is after decades of staring reality in the face, this is not merely the result of younger people tending to put more emphasis on environmental factors than old codgers do (although that would still make sense in this 'theoretical framework', since younger girls are less likely to have had children than their mother's friends are). The same pattern holds across age groups. Among women between the ages of 18 and 35, 16.8% of those with no children emphasize genes, 18.4% with one child do, and 25.0% of those with two or more kids do.
Because men are less selective of their mates than women are, it's not surprising they are also less attuned to genetic influences on personality than women. Further, men rightly feel they have more individual influence over their objective desirability in the eyes of the opposite sex than women do. But fathering causes men to be more perceptive of innate differences in people as well. The percentage of men who believe genes play a primary role in determining personality by number of children (N = 1074):
GSS variables used: GENEEXPS, GENDER(1)(2), CHILDS(0)(1)(2-8), AGE(18-35)