It's interesting how these things vary from person to person -- I can only do it (for the short distances that I can) when I'm providing that constant "input" to the pedals from my legs.

Next time, watch the professional riders at the Grand Tours on television. Their bikes do not have relaxed geometries and they can still ride with no hands. You will see this with the domestiques as they fumble around with water bottles, etc.

At the final entrance to Paris, they even drink out of champaign glasses. At other times, riders call up for a small can of Coke and use both hands to pop off the tab.

I think It's not so much pedaling or not, but either way you need to have enough speed to be stable, and a lot of weight on the pedals. If your feet aren't loaded up then you can't really transfer your weight side to side. Try it either mashing, or with one foot extended.

I was thinking, wouldn't riding hands free be like.... well, like riding a bicycle? Once you learn how you never forget. In my case however, I never learned how to ride hands free weighing more than 200 Lbs. The other factor that might play into it is that both my current bikes are carrying a lot of weight on the handlebars I never had when I was a kid. Lights, trigger shifters, Ergon grips, bar ends, mirrors, computer and a handlebar bag.

I also mash when riding hands free, I think it may help because slightly altering the pressure on each pedal can be used to correct minor imbalances... at least that's how it feels. i also need to focus on a point around 20 feet ahead of me, if I focus down towards my wheel I tend to fall.

I ride hands free every day due to it allowing my hand numbness to be controlled. The key to me on many road, touring and MTBs is the frame/fork alignment and headset maintenance, as stated earlier. A check I do that shows frame/fork alignment issues is to hang the bike upside down from two points spaced at your dropouts with string around each wheel. If the fork and frame are not close to in line you can not ride hands free. Having (2) mountain bike that are not straight would not be unusual IME.

My Trek is definitely tracking straight and I just did a frame up overhaul including a new headset and a fork upgrade. In all it's various configurations over the years since buying it new I have never been able to ride it hands free. The "beater"? I've never checked but it handles really well, it's days are numbered though, it's hybrid replacement should hit the road later today and once it's all dialed in the beater gets stripped of it's goodies and prepped so it can be put up for "adoption" in the Spring. After I have all the extras off it I'll give another try at hands free on it.

Fast forward 3 hours: Got the hybrid together and took it out for a test ride, tried it hands free and was able to do it for a short distance. Didn't want to risk going farther until I have some more seat time on it.

In the early 1980s I lived in West Philadelphia and rode a coaster brake bike that I pulled out of the trash. I would regularly ride that bike no-handed from 3rd St. to 44th. St, down Lombard & over the South St. bridge, never touching the bars.

At the same time I had a Legnano racing bike. I don't remember riding that no-handed! More recently I had a Trek 520 - very difficult to ride no hands. For a real joke, try riding a Brompton no handed!

Then a few years ago I got a Thorn Nomad. Not a feature I'd given any thought to, but I was very happy to discover that I can ride that no-hands pretty much indefinitely. I have had it shimmy a bit with an awkward load, but that is very unusual. I, too, find it very useful to ride no hands now and then on a long ride. I interlock my fingers and stretch them overhead or stretch them behind my back.

I have no trouble at all riding my trike hands free. I just put up the kick stand take off and then let loose of the handle bars.

Maybe the OP did not realign his front wheel correctly with the frame after fixing a flat or something. Riding with no hands is easier than you think and anyone can do it when the wind is calm. Try it with more speed, and try looking further down the road. Balance will greatly improve.

I think some of the difficulty some people have with riding no hands has to do with misunderstanding how a bicycle steers and maintains its stability. You do not steer a bicycle with your handlebars. You steer a bicycle by shifting your weight, and compensating with the handlebars so that the point where the wheels hit the ground is below the center of gravity. If you only turned the handlebars and did nothing else, you would crash because the wheels would steer out from under you. If you push a bike with nobody on it, it will stay up and self-correct to some extent because when the bike leans, the handlebars will swing around to steer the wheels back under the center of gravity, as long as it maintains enough forward momentum to do that. When you ride no hands, you basically let the bike do that and at the same time compensate with your weight so that all the corrections result in going the way you want to go.

Of course, when you think about it that way, it's a horribly complicated thing that sounds like it takes years of practice and lots of talent. But it's really the same kind of correction you make subconsciously all the time just to be able to maintain your balance as a biped while standing, walking, etc. Basically, if you think that you steer by turning the handlebars or that all those corrections are something you have to consciously micromanage, you will have a hard time riding no hands. If you can let the bicycle stabilize itself and correct for it the same way you do when you stand on one foot, it's much easier. So I guess in some cases, it might be in your head.

One of the quickest ways to make a bike impossible to ride with no hands is tightening the headset so that it doesn't swing freely. It's counter-intuitive, because at first you might think that in order to not go all over the place, you need the handlebars to stay pointing straight ahead. But actually that's the opposite of what you need. You need the bars to be able to swing and make minor corrections by themselves. If the headset action is stiff, those corrections are sluggish and and you go all over the place.

The load and the front end geometry do matter, though. I can ride my touring bike with no hands when it's fully loaded, but only if the load is evenly balanced on both sides and only if I keep my weight back. If I lean forward, the front end shimmies. I can ride my commuter bike with no hands with a fair amount of weight in only one pannier, but as you can imagine, I have to lean way off to one side to counterbalance it. On my brevet bike with no hands I can fish around in my saddlebag, take out a jacket and put it on, steer around potholes, grab a bottled beverage and unscrew the lid to take a drink, etc.

I think that on most road bikes, the geometry should allow for a reasonable amount of stability given the weight distribution of most riders. But if the headset is stiff or the cables are routed in such a way that the movement of the bars is in any way impeded, it won't work.
I generally think I'm pretty good at riding no hands - I do it a fair amount without thinking, even doing no-hands trackstands at stoplights on my commuter with one pannier. But I've ridden a fair number of folding bikes with small wheels or upright cruiser bikes that I could not ride with no hands. We have an xtracycle attachment mounted to a MTB frame, and I can't ride that with no hands, whether it's loaded or not, even though otherwise it feels extremely stable to ride.

I'm 60 years old and I have no problems riding hands free, though for some reason I can't do a long track stand like I use to when I was in my 20's, 30's, and 40's.