I don't think they mean give their children their own space, I read that as parents allowing children into their own personal space, ie including them in their hobbies, allowing them to use and play with things they use etc.

My personal experience also doesn't seem to line up with this. I often see men excited to teach kids about their hobbies or expose them to things they're interested in. Sometimes things are just too fragile or too dangerous for young children to help with, but I see both men and women steer kids away from that stuff.