It seems strange, right? But that's apparently how it went. The toga praetexta was associated with the most important magistrates, and most think that kids wore it as a form of protection from harm or mischief. It had a certain reverence attached to it, like a modern day priest's habit, maybe, or a very expensive suit. Or, it's very similar to colonial British schoolboys walking around India in their Sunday best. It announced importance or inviolability? That's the better way to think of it: not as a kid's costume, but as an important adult's costume put on a kid. In public life, you would not see kids wearing it all that often, since they generally kept to the house, or at least were not running around in the forum every day. Macrobius has a lot to say about the praetexta, if you believe it, and he says that the son of Tarquinius Priscus was the first kid to wear it, and that because he had killed an enemy in combat. Then supposedly it just became a tradition. If true, it might have started out as a mark of special honor which somehow became default for all kids. I suspect it might have had something to do with kids in its original context, which was in the bizarre Etruscan culture, and its use and meaning became a bit confused as it was transferred to Roman practice.