There are two things that I think stirrings could be. 1. Is a wet dream and feeling for someone that they want to stop because they want to control the population and it’s already someone’s job to have kids. That would ruin that job. Then slowly ruining other jobs. It’s like a pyramid made out of cards. One falls and the whole thing is ruined.

2. Maybe stirrings are you stirring in your sleep. Waking up from blindness of the fact that not everything has to be perfect. Not everything-down to the tiniest detail-has to be regulated. I think stirrings are you waking up from the grasp of the government and wanting freedom from the outside moment. Maybe its realization that there’s something beyond their world and beyond anything they know.
In an additional (bonus) page in Divergent, it says that Veronica Roth’s (author of the Divergent series) hero is Louis Lowry’s book the Giver. They are both similar stories. A Utopian society with rebels crawling everywhere, an unknown outside world. Some other things too. That’s my AHA moment. Where I connected those two stories.
At the House of the Old, they stop taking pills. I think it’s because of the fact that they’re too old and not able to get that freedom. So stirrings happen to them but aren’t able to find their way to freedom from the government.