I completely get it that people with children refocus their whole life around their child. It's totally natural, and I applaud it and support it. I have had friends that I spend less time with because they have other - far more important - priorities in their life.
What I find annoying and offensive is when parents think that in addition to THEM being obsessed with their child, I TOO should be interested in their child.
Why should I want someone else's kid to be a part of my life? What interests will we have in common? I mean sure, I like toddlers, they are fun, but I'd rather play with a puppy than a toddler. Why do you think I have an obligation to be interested in your spawn? It's a separate human being, I might like your kid, but I might loathe it.
Why do new parents lose so much empathy with the rest of the world? I totally get it that the video of your child doing something funny is something that you treasure, but why are you so insensitive that you think that I will find your child fascinating and want to see photos and videos of it. Newsflash - other people's kids are usually boring.
Key disclosure: my wife and I can't have kids. We've accepted that, and we spoil our nieces and nephews and spend as much time with them as we can. But new parents are always egocentric / world-revolves-around-my-spawn / insensitive / un-empathetic. And they have no idea they are doing it even.