Post only about your kids and nothing else? You could be a competitive parent.
On a more positive note, posting about children may indicate beneficial mental qualities. The same study that analyzed the connection between social media posts and facets of personality found that people who mostly post about their kids tend to be more conscientious. They are more likely to be organized, hard-working, and responsible, and usually use platforms like Facebook less frequently than their peers. They prefer discretion and try to keep away from gossip.
However, there were also indications that such individuals may post excessively about their children as a form of “competitive parenting.” This, again, goes back to validation: some parents think they are failing their children and so post their kids’ achievements and other positive things to make them look and thus feel better about themselves. This over-parenting behavior can also bleed into their other posts, such as sharing information about safety or the community in an attempt to parent others.