Well, if the US employers force their employees to get it to avoid 2 weeks of downtime, that would suggest that there’s evidence that it works. If the employee got the shot - but got the flu anyway (wrong strain, or it truly didn’t work), the employee would be in NO condition to get to work.
When Moon Unit was 1, I had had a flu shot. That year, a lot of people who got the shot, got the flu anyway. I was one of them. I felt like crap for 5ish days, though that improved once I got antibiotics for the secondary respiratory infection. The worst day was when I was lying in bed, covered by all the blankets we owned, shivering, as my temperature spiked. Had someone burst into the house waving a rifle just then, I’d have been happy to see him. It was at least a full week before I felt even remotely human.
Naturally, the kids had the same thing (in fact, my son gave it to me). As they were being cared for at home by a nanny, they ignored the nanny and wanted MOMMY. When Mommy wanted to be left alone to die in peace. No such luck.
Your husband is being a jerk. I’d suggest that if he’s sick with the flu, he still has to take care of the baby. That’ll teach him! (of course, you’ll have to step in during the worst of it; I could not have cared for the kids when my temp was spiking).