The main reason is that bicycle tyres are much, much thinner than car tyres.
A little tetrahedron of broken glass or a drawing pin that would puncture both tyre and tube on a bicycle won't trouble a car's tyre in the slightest.
A secondary reason is that bicycle tyres with tubes have additional ways to suffer punctures: an under-inflated tyre is susceptible to pinch flats.
It's pretty much as simple as that.
bicycles.stackexchange.com/users/43808/Daniele Procida
An unaddressed reason is speed-induced wind and the shape of modern roads.
Motor vehicles travel in a lane, and a roadway is generally two or more lanes in opposite directions.
As such, these two lanes meet at the centerline, which tracks the highest point on the sealed road surface.
For drainage, the road is not flat - all roads are intended to have some minor slope to assist rainwater to flow off.
Also, some corners are cambered, so that the shorter inside of the corner is lower than the longer outer edge.
Bringing it back to the question - we cyclists do not generally ride the centerline.
I ride on the outside of the road, which is where road detritus gets washed by rainwater, and debris also gets pushed here by the passage of cars.
You can see a similar effect on a flat road just before a traffic island - here's an extreme example, which is mostly gravel and organic leaf matter.... ...
but I'd expect to find metal wire shards in there and possibly fragments of glass and plastic.
Nails, screws, and staples are normal road rubbish too.
Basically anything that can be "swept" by the passage of vehicles travelling at 50 or 80 or 100 km/h which creates a respectable breeze to sweep the lane clear and push the jank downhill to the sides.
The side (or shoulder) of the road is where we end up riding.
All of these items lie on the road surface, and get concentrated on the sides, and this contributes to punctures along with the other points raised in other answers.
bicycles.stackexchange.com/users/19705/Criggie
Essentially all modern car tires have steel puncture-protection belts under the tread surface
bicycles.stackexchange.com/users/49627/Armand
As someone who's had three car tire punctures in 200'000 km, and one bike puncture in maybe 20'000 km, I'd say an individual result is simply not statistically significant.
With a car, if you do mostly highway and city driving, punctures are rare.
If you go on mountain or country roads, of frequently visit construction sites, railroad depots, junkyards and the like, you'd better have a spare tire ready.
The same is true for bicycles: going all-terrain is not the same as riding on dedicated bike lanes.
Other than that, causes of car and bike punctures actually have not that much of overlap.
Small glass shards which damage a bike tire are not a threat to cars, and sharp rocks / metal scraps which are dangerous for a car tire can be easily avoided on a bike.
bicycles.stackexchange.com/users/23891/Dmitry Grigoryev
There are puncture-resistant versions of popular road bike tires.
I've got some on my bike from a well-known brand as I bought it
and I haven't had a single puncture yet.
For the same distance I would have expected 3 or 4 punctures on the tires I used previously.
However, this comes at a cost - higher rolling resistance.
Using the site linked below, I see a 9.3-watt power loss versus the race tires of the same brand at 8.3 bar pressure.
At lower pressures, the power loss is higher.
I'll probably get different tires when these wear out.
Conclusion: it's possible to make bike tires more puncture resistant, but at a cost.
It's much easier to change the tubes on a bicycle than to change the tires on a car, so the trade-off for bicycles is different: people prefer to go faster with the occasional additional puncture.
Site that has a Rolling Resistance Test Result comparison option
bicycles.stackexchange.com/users/19232/Erwin Bolwidt
I have driven in my life 200 000 km by car and 20 000 km by bike. In my car, I have never had a single puncture. In my bike, my puncture count probably exceeds 5.  Why do bicycle tires suffer from frequent punctures whereas car tires do not?
Why do bike tires suffer from frequent punctures whereas car tires don't?
bicycles.stackexchange.com
<puncture><bike-vs-car>
bicycles.stackexchange.com/questions/69225
bicycles.stackexchange.com/users/33932/juhist
Bike tires puncture more than car tire because they are thinner. Moreover, an under-inflated bike tire is susceptible to pinch flats.  There are puncture-resistant versions of bie tires but they are more expensive. Furthermore, bikeS travel more frequently in areas where sharp objects are likely to be found like off-road, edge of main roads, country roads, ETC. Bike tyres are much thiner and less reinforced than car tyres, so they are much more sensitive to small sharp pieces of glass or other material. Reinforcing the tyres carries a penalty in weight and rolling resistance that reduces speed more on a bike. Bike and car tyres are threatened by different hazards, and the risk depends on the type of surface travelled on. Even on the same road, debris tends to get swept away from the centre and onto the part used by bikes.
Bike tyres are much thiner and less reinforced than car tyres, so they are much more sensitive to small sharp pieces of glass or other material. Reinforcing the tyres carries a penalty in weight and rolling resistance that reduces speed more on a bike, Bike and car tyres are threatened by different hazards, and the risk depends on the type of surface travelled on. Even on the same road, debris tends to get swept away from the centre and onto the part used by bikes.