I have to get this math problem right to receive an A in the class. The problem was something like a circle inscribed in a hexagon. The answer was 2:3. I got 3:2. I must come up with an argument that it didn't matter so I can get the problem correct! It might be impossible, but I'm sure my teacher can be convinced by a bit of wordplay haha.

Ratio: The relative magnitudes of two quantities ([can] be expressed as a quotient).

Well, I am not sure there is an argument. In both ratios, one number is 1.5 times another. But relative to all other ratios (1:1, 2:4, 4:2, 11:7, etc) they (2:3, 3:2) each represent to different ratios.

2:3 is a smaller ratio than 1:1. And 1:1 is a smaller ratio than 3:2.

Another way to look at it is:
2 cups sugar and 3 cups flour are not the same as 3 cups sugar and 2 cups flour. But
2 cups sugar and 3 cups flour are the same as 3 cups flour and 2 cups sugar.
I hope that makes sense.

It seems like grades are important to you. That is great. Some people do not care between an F and an A, but you do. I commend you for that. My advice is don't get too caught up in grades, even just academically there is more to school than grades (like learning something and then applying it to your life). Ask your teacher to help you understand why there is a difference between 2:3 and 3:2.