Why do some people cycle with their knees sticking out to the side instead of parallel to the frame?
Based on the people I've seen riding, knees-apart is a symptom.
New rider - it takes time to develop a good pedal stroke, and some people haven't got there.
Saddle too low - If your position is really bad, then the knees instinctively separate. I have no idea why - try riding a way-small bike. Relates to....
Posture - riders who might remember the Moon Landings might be expecting to sit up quite straight (ie Dutch-style bikes) where the back is almost vertical. To do that on a modern hybrid bike needs a low saddle, which encourages the knees apart.
Fear of falling - Saddles can be set down by riders who want to put their whole foot flat on the road while stopped. Yes this is a saddle-too-low, but the root cause is poor balance, or a perception of the same.
Beer gut - I was over 100 kilos when started riding seriously on a road bike, and to use the drops I had to be standing out of the saddle, else the belly and the upper thighs tried to occupy the same space. Even a minor tum will affect the upper thigh and where the skin folds to the lower tummy (technical term anyone?)
Thunder Thighs - related to the stomach one above, but simply lower. If the rider's thighs are a bit thick, then repeated rubbing on the sides of the saddle's nose may be an irritant and drive their thighs apart. Chaffing is no fun.
An unfortunate choice of clothing? I've done rides where something wasn't sitting quite right, and to alleviate irritation have sat up or rearranged things like seams. This would be a more temporary situation.
Moisture - poor clothing choices can build up sweat in all sorts of places. Dampness could also come from rain or from road water and poor mudguards/fenders leading to damp clothes.
History - riders who have come from a MTB or BMX background may be subconsciously prepared to stick a foot out and dab. That's where they do a light touch on the ground to help with balance on a corner.
Speed - Sitting up and spreading yourself out catches more air to slow you down. If you're going too fast then this is one way to reduce speed. Again, more subconscious than planned.
Have I missed any?
- Balance - I know I've used my knees like a motorcyclist on a turn, to vary my "lean" quicker. Probably not pedalling at this moment though.
it might be for therapeutical reasons.
once I hit a pole with my knee and it hurt. I asked a physiotherapist how to ride until it gets better (I had to because I was working as a messenger) and I was told to stick my knees out. it did help.
the other explanations given by @Criggie may be more frequent, but this is a valid reason too.
My right knee sticks out because my right hip is so tight that I cannot bend my right leg into my chest straight - it has to go out of line to do it - so this is the same on the bike. I have always had this problem and I believe it's probably from years of sitting with my right leg underneath me. It causes great issues in cycling because I lose a lot of power in that leg and I can't ride in the aero position at all.