There are several things that give manual mowers an advantage over the traditional petrol mower:
Never have to buy fuel for it
No smelly exhaust fumes
Carbon emissions are virtually zero after manufacturing emissions
Never have to empty a catcher or deal with clippings, apart from a quick sweep of paths afterwards
Healthier grass as cuttings are dropped back onto the lawn the way the grass is cut is much healthier for it and causes less impact and stress
Much quieter, you can easily talk over it and be heard and hear others
Kid friendly, much safer, less risk of flinging rocks at high speed
The blades stop cutting when you stop pushing, this means that you can stop if a child comes near
It’s completely silent when you do stop pushing
It’s much lighter to push, as long as the grass isn’t too thick
It’s light enough and thin enough to hang on a wall
disadvantages
Of course there are disadvantages as well:
Long or thick grass is harder to cut, you have to cut much more frequently than a petrol mower
Damp grass is harder to cut as the wheels can slip
It’s harder to cut near the edges of gardens, and around trees and post (though I have seen models that can cut right up to a garden edge)
When you stop pushing it stops cutting, which can make inside corners a bit harder to cut
Some long strands might be missed as they get push over rather than cut
You can’t use the full cut width most of the time. I generally use about half as it gives good overlap.
Need to adjust cutting blade distance every now and then
Weed seeds don’t get picked up in a catcher
Everyone thinks you’re crazy and/or too poor to afford a real mower
The needed overlap means you have to walk a bit further, but I don’t mind so much as the mower isn’t as heavy as a petrol one, it’s not as noisy so it’s not as tiring, and you don’t have to keep stoping and bending over to empty a catcher.
photos
Here’s some photos:
Flymo H40 in action
Hanging on wall
The back roller adjusts height of the cutting blade off the ground and
the length of the cut grass. There are four settings. Apparently there's
a bolt you can move to get more, but the default is fine.
Intersection of the curved rotating blade and straight cutting blade.
This cutting technique is very similar to normal scissors. The spinning
blades are blunt, all the cutting is done by the stationary blade.
videos
Here’s some videos that show how it works and one of me cutting some grass.
Spinning from above. Both wheels can drive the spinning blades, here I’m turning only the left wheel:
Cutting grass. It’s a bit nosier than normal as I had the blade touching so I could cut paper in the above video. The grass had only been cut two days before but as it had been raining and quite humid the grass was growing very quickly anyway. Normally I only cut it once a week, which is sufficient. My 4 year old son was also helping me with his plastic mower: