He has very poor social skills and is very self-centred.
If I was in your situation and wanted him to change, I'd have given him a 'basic conversational skills' talk long ago e.g. 'people like to be listened to and to get the impression you are sympathetic. They don't just want advice, or to hear about your experience straight away. Conversation is two way, so by all means contribute your experiences but think first about whether they are relevant and helpful and, you need to contribute equally to listening, too, otehrwise it's just two people talking at each other.'
I'd have emphasised the particular delicacy of baby-related topics and the need to think extra carefully before speaking.
Then, when it happens, I'd roll my own eyes and gently show him up, 'yes, DH really hasn't grasped that all pregnancies and babies are different, as we we've been so lucky so far. Of course he also hasn't had to grasp half the work it took even with our easy babies, as he was asleep or out at work most of the time!'.
If you don't look embarrassed, or apologise for him to your friends, they will think not only that he's a naive, lazy, poor father but that you are a total mug who he's conned into doing all the work with a bit of simple flattery.