From both bride and groom:
* They don't think ceremonies in particular are fun for kids and they don't want the disruption.
* The reception has alcohol and they're concerned about liability, while also wanting their friends to be able to relax and have fun. It creates a permission structure to get a babysitter.
* Cost. Weddings are more expensive than ever and including kids explodes the numbers for a lot of families. They can afford 100 people, they have 150 people expecting an invite, and making a decision like 'child-free' helps them work that out.
* Some parents do not handle their kids and that can lead to disaster. In that case, a whole wedding might go child-free over one cousin's children.
Like most things, some people are being jerks, though. Don't like kids, don't want them there, and then get mad when the parents say "I can't leave my 3-month-old breastfeeding baby, plus you invited all my babysitting options TO the wedding, so now I can't go."