0 degrees Fahrenheit and 0 degrees Celsius aren't the same temperature.

Instead 0°C = 32°F

Yeah but 100c is boiling point, and 212 is boiling point, so half the boiling point of one should be half the boiling point of the other, right?

Using terms such as "half the temperature" become meaningless statements unless using a temperature scale that starts at 0 at absolute zero.

Celsius degrees and Fahrenheit are both different amounts (a difference of 1°C is a difference of 1.8F,) and the scales start at different places (0°C is 32F.)

So the actual conversion formula is that you have to multiply by 1.8 and then add 32.

Also, for every 1°C increase of temperature, you see 1.8°F increase. Not only do they not share a zero point, they increase at different rates. The only point °F = °C is -40. At any other point, if you were to plot temperatures in celsius and Fahrenheit, they'd be two straight lines diverging from eachother, the further you got from -40.

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there's a flat gap between the two temperature scales. What you're doing there is applying the wrong logic.

following your reasoning, 50C = 106F, so 25C = 53F, so 1C = 2.1F.

it's a logarithmic curve

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Because the calibration points for both scales are based on the state changes of water.

At standard pressure water melts (changes from solid to liquid) at 0°C / 32°F.

At standard pressure water boils (changes from liquid to gas) at 100°C / 212°F.

Since both scales are linear, 50°C, which is the midpoint between 0°C and 100°C, is equivalent to 122°F, the midpoint between 32°F and 212°F.

Because the freezing point is at a different temperature on the two scales. If both used 0 for freezing, then half of one would be half the other. But because of the offset, they do not stay linear with each other.

In other words, if (degF = A x degC), you would see the kind of relationship you posted. But instead, (degF = A x degC + B), where A= 1.8 and B = 32. That “+ B” throws everything off.

Correct. Consider that in Fahrenheit, 212 is boiling and 32 is freezing. 212-32 - 180. So the halfway point between freezing and boiling in Fahrenheit is 180/2 + 32 = 122 degrees. 122 degrees Fahrenheit is in fact the same as 50 degrees Celsius.

The scales have two major differences between them - their degrees aren't the same size, and they each have different starting points. An increase of one degree Celsius is a bigger change in heat than one degree Fahrenheit (1.8 times as much), so there's a specific ratio between the two. And the Celsius scale sets its zero point at the freezing point of water, while the Fahrenheit scale sets its zero at a particular chemical reaction of ice and ammonium chloride (called a frigorific mixture), because it was consistent to reproduce and always comes to the same temperature.

So the conversion from Celsius to Fahrenheit, you multiply by 1.8 (the ratio between their degrees) and add 32. And going from F to C, you do that backwards - subtract 32, then divide by 1.8. So 50°C using that formula gets us to 122°F.

From freezing to boiling in Celsius is 0 to 100. Halfway is 50.

From freezing to boiling in Fahrenheit is 32 to 212. Halfway is 122.

What's 50C in F? It's 122!