Unless you are female, which is the salient point of the article. Mothers show a gender bias towards their daughters, whereas middle-age men don't appear to have a gender bias.
Figure 1a (best friend) is basically symmetrical: gender bias of the best friend is opposite sex. The bias peaks for women at 27 and for men at 32, gradually decreasing until the best friends for both are slightly female-biased in their 70s.
In Figure 1b (second-best friend), the 2nd-best friend for 20-something males is another male. The bias gradually declines until by 40 his second-best friend is 50/50 male/female.
But for second-best friends, "women show a striking reversal" from same-sex to opposite-sex. A 20-something female's 2nd-best friend is also female, but it strongly reverses towards males (peaking in her late 40s).
If my interpretation (of their interpretation) is correct, these graphs are showing that a female's best friend is initially her husband, but he is gradually replaced by her daughter: "the younger (25-year) peak for 50- year-old men is half that for women and shows a more even sex balance, whereas that for women is strongly biased in favour of female alters (presumably, daughters)". The husband, in turn, falls from 1st-best friend to 2nd-best friend (replacing the formerly female one).
"Finally, fourth, our results provide strong evidence for the importance of female matrilineal relationships in human social organisation. There has been a tendency to emphasise the importance of male-male relationships in an essentially patrilineal form of social organisation as defining human sociality [20], but our results tend to support the claim that mother-daughter relationships play a particularly seminal role in structuring human social relationships, as has been suggested by some sociological studies [21]."
EDIT: attempted to increase clarity. Not sure what the HN takeaway is.