Why are bicycle gear ratios computed as front/rear and not the opposite?

When talking about bicycle gearing, the overall theme (in my mind) is translating rotations of the crank to distance traveled. Historically, I believe this was used to translate the gearing of "safety" bicycles (what we now ride) to the size of the larger wheels on the old penny-farthing highwheelers. In that case, you multiply the gear ratio by the wheel diameter to estimate the equivalent penny-farthing wheel size.

Nowadays, using the chainring as the numerator lets you multiply the gear ratio by your cadence (rate at which you're turning the cranks) and your outer tire circumference to compute your speed.

You could easily flip the ratio if you wanted. But now to compute the speed you'd multiply your cadence by the tire circumference and the divide by your inverted gear ratio.

On a car, first gear might be 5:1. Five (input) rotations of the crankshaft for one (output) rotation of the propshaft. This tells you nothing of the number of teeth that are actually used on the gears. One a bike, we express the gearing in terms of teeth front and rear, eg 39/13. Not the number of rotations. This is more useful for calculating gear-inches or development, which is how we normally express ratios--if we expressed the gear as 13/39, we'd then need to take the inverse of that before calculating gear-inches anyhow: 1/(13/39).

In brief, rotations:tooth counts::apples:oranges

Right now we have a single standard of frontteeth:rearteeth like 53:11 and 30:34, which has been around for many decades. But does not account for wheel diameter or crank length.

So we get another standard which is Gain Ratio

And we still have an old-school notation of Gear Inches from the high-roller bikes so there's some consistency over time.

Additionally metres/yards/feet developed (per crank rotation) is known as Development or Rolllout are a more recent way of showing the same info, along with RPM at speed X and speed at RPM Y

Ultimately it comes down to tradition - early bicycles had a fixed chainring size and perhaps two cogs on a rear hub that could be flipped. So your gear ratio was stated with the fixed unchangeable part first (ie you wouldn't swap chainring on a ride, whereas you might flip the rear wheel for the other gearing.)

Some people use Percentages but that is specific to a cassette and has no bearing on the chainring side of things.

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And also because https://xkcd.com/927/ If you choose to flip an existing standard around, absolutely utterly make it unique in notation to avoid confusion. A hypothetical "11:53" is not the same as 53:11 and imparts exactly no more useful information. Do read and understand https://xkcd.com/1179/ and comprehend just how much enmity people who use YYYY-DD-MM earn themselves.

The front-over-rear ratio for the drive train on a bicycle describes how much faster the rear wheel turns than the rider's cadence.

The rear-over-front ratio for the drive train on a motorcycle describes how much more torque the drive train can produce at the rear wheel than at the motor.

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It is of course matter of convention which is used, but I would posit that because

1. To the rider, the bicycle is a mechanical augmentation of the human body and
2. In locomotion, the human body is speed-constrained rather than force-constrained,

the ratio that describes how much more speed the bicycle allows is the natural measure of its drive train.

Conversely, I would posit that

1. To the rider, a motorcycle is a means of turning fuel into motion, and
2. Internal combustion engines are better at producing speed than they are at producing torque,

so that the ratio that describes how much more torque the drive train produces than the raw engine becomes a more natural measure of the drivetrain.