My little girl just learned this past summer. She’ll be seven in December. She’s had a swingset since she was four and played on it regularly, but we always had to push until one day she just started doing it herself.
My son is seven and he just got it recently. My daughter is five and she hasn’t figured it out.
As has been said, they are all different.
My little boy was riding bikes without stabilisers when he was 3, but doesn’t do jigsaws and refuses to write his name and can’t swing himself at 4 1/2.
His sister was swinging at 3 but didn’t learn to ride properly until nearly 6 but was putting together 30 piece jigsaws at 18 months.
If you worry about individual accomplishments too much or compare one against the other like for like it’ll drive you mad.
Are they happy and active? that’s all you need to worry about.
I have a kid in my third-grade class who can only do it if you get him started with a couple of pushes. Not something to worry about unless you really like to worry, IMO.
continuance of minor hijack
I’m from the Midwest (Michigan) and we always called it pumping.
My daughter turns 6 next weekend and still doesn’t get it.
She’s fine. She doesn’t care to learn, that’s all.
You’d think, wouldn’t you? Unfortunately, this is another in the (very long) list of Parenting Duties that seem so very easy until you try it. Some kids pick up on it right away. Some stare at you like you’ve grown a cactus out your butt…
The average age for this generally unnoted milestone seems to be about 5, based on a couple of books in my collection and a lot of years of observation. But, as for all averages, there are plenty perfectly normal kids who skew the number down, and others who skew it up. As China Guy said, it’s only something of concern if it’s part of a larger pattern of missed milestones or developmental delays. A 6 year old kid who can’t pump or walk a balance beam 6 feet or stand on one foot for 10 seconds…not a big deal. A kid who can’t pump *and *can’t walk a balance beam 6 feet *and *can’t stand on one foot for 10 seconds…now we’d better look a little closer to see what’s goin’ on.
Midwest (Chicagoland) here, and it’s been “pumping” since at least the mid 70’s. 
This is actually the first time I have ever thought about this, but I suspect that my husband would not be able to generate momentum to swing. We don’t have kids. His parents were not even remotely playful people and it’s unlikely he ever got on a swing as a child. His father is/says he is extremely prone to motion sickness, and my husband claims to have this same ailment (which mysteriously fails to kick in sometimes when he is having fun with something that should have him barfing…but that’s a different topic). His mother protected him from absolutely everything in the world and it seems likely that if he eyed a swing as a child, she would have told him no, he couldn’t go on it because it would make him sick like his father. This would explain why once when I instructed him to “scootch” himself forward, “you know, like you do on a swing,” he was clueless about what I meant. Maybe he is the oldest person who can’t swing back and forth.