A friend of mine just posted on Facebook an incident in which someone berated her for "missing out on precious moments" with her child because she was checking Facebook while the child played. Now of course, in an age of social media, it is easy for parents to become absorbed with online trivialities at the expense of building a relationship with their children. But a stranger is in no position to know if a parent is doing this simply because she happens to be using technology at some particular moment.
What strikes me about this particular meme (which I've seen before--there are online articles that have gone viral expressing this idea) is the commodified approach to time it expresses. Economists speak of "opportunity cost": if you do X rather than Y, you are "paying" the opportunity to do Y for the sake of doing X. And obviously this is true, in the sense that, as Chesterton put it: "Every act is an irrevocable selection and exclusion. Just as when you marry one woman you give up all the others, so when you take one course of action you give up all the other courses. If you become King of England, you give up the post of Beadle in Brompton. If you go to Rome, you sacrifice a rich suggestive life in Wimbledon." But for Chesterton this is about drama and adventure. The problem with the "missing out" argument is the assumption that "moments" with one's child are some sort of possession which one should covet greedily if one has the right priorities. While it sounds like a glorification of parental love, it actually treats the child, and the parent's relationship with the child, as being valuable for what the parent gets out of the relationship. The parent could have X number of "precious moments" but is settling for X-n.
In fact, children need some time to play by themselves without the parent hovering. Parents who insist on being involved with every moment of the child's lives are refusing to allow the child to develop any degree of independence. It is control under the guise of love. This is how we get "helicopter parenting."
I'm sure that most of us who are parents could do with spending more time with our children and less time on social media. But it's not because our children are a source of a finite commodity called "precious moments" of which we should be greedy. It's because they are human beings, worthy of our love and attention and respect. Sometimes we show that respect by putting down our computers and spending time with them. Sometimes we show it by leaving them alone.