My son's daycare hosts a number of events throughout the year where parents will inevitably take photos. The more photos we take, the more photos we have of each other's children. Of all the pictures I've taken, I'd say about 30% are "Facebook appropriate"; meaning, there are no children in the photos whose parents might object to my posting their children's likenesses on the social network.
Instead of asking every parent in the daycare, I silently respect others' privacy. Not everyone does this. Hence, Facebook photo flagging.
People flag the photos because they feel violated when someone else posts photos without their permission. I'm willing to bet the most frequent offenders are family members and friends who post photos of others' children, thinking they don't have to get the parents' consent.
Problem is, Facebook doesn't remove photos just because a user tells them to. It's up to the user to convince the original photo uploader to take it down. Facebook gives you the option of contacting the offending party directly with a message asking them to take down the photo. There is no guarantee the photo will actually be removed.
But all is not lost. You can take preventive measures on your end:
Customize the privacy settings for each album you upload. If you're concerned about a certain Facebook "friend" sharing the photos you post, block them from seeing the photos by clicking on the gear tab and opening the privacy settings.
Update your privacy settings for tags. It's possible to make it so no one but you can see photos you are tagged in.
Indicate a photo is your intellectual property. When you report a photo, indicate the photo is your property if said photo depicts minors under the age of 18 (your children) without your consent. Then, you will be reporting the photo as a copyright infringement instead of abuse. Just click on the link at the bottom of the report window that asks if the photo is your intellectual property. The link will take you to a page that outlines the procedures for taking this reporting route.
Don't post photos you don't want shared. Simple enough, right? If you're that concerned, why not email photos to your trusted friends and family members instead?