It's been awhile since we've recapped this, so let's just put this out here again for general knowledge purposes:
Baby Shower = bridal shower
Birth = wedding
Birthday parties = anniversary parties
Meet the baby parties (sort of)= birthday parties (in the sense that it is basically the birthday party for the birth). They would also (kind of) = wedding reception.
You can host your own wedding because it is a life event that you want witnesses for. I suppose you could host your own birth party if you really wanted to.
Hosting your child's birthday party is hosting a party in their honor, much as someone else (mother, sister, friend) hosting a shower for you is hosting it in your honor.
As adults, how many people host birthday parties in their own honor? Usually it's either an invitation of "hey---I'm throwing a surprise party for (guest of honor)" or "Hey, I want to invite you guys over for dinner". As an adult, the company of someone's friends/family is the general (gift) expectation and is not specifically a gift-giving event.
A quick way of telling whether or not it is a gift-giving event is if it would be weird/rude to receive an invite with a registry link. How many birthday parties have you received that have had a registry? Wedding invitations should not have registries, nor should birthday parties because these events are not specifically gift-giving events. Many people do give gifts because they would like to, but not because it's expected of them.
A meet the baby party is a party being held in honor of the child that has been born and is not explicitly a gift-giving occasion. It's probably closer to a "birth party" in the wedding comparison I made above.
Would you ever send someone an invitation that says "Hey, buy me stuff and come over to celebrate me?" No, most people wouldn't. Therefore, hosting your own shower is not acceptable.
Stay tuned in the future for the review as to why second showers are not ok. :-P
(You can thank my pinched nerve in my back and my sleeping toddler for the time spent on this post. There's not a lot to do when you're spending most of the day reclining on the couch on a heating pad.)