Truth be told, they didn't base this gross assumption on anything like science. They used fractal calculations to make the presumption, but didn't go out and gather up every snowflake and look at them and take pictures and do sketches and compare them. No! They just dismissively waved their hands at it and said no two snowflakes are alike.
It's dinosaur thinking like this that keeps us entrenched in 19th century technology and inhibits us from doing really cool Star Trek stuff.
I will now prove that not only are there two snowflakes that are alike, I'm going to conject that there are triplets and quads out there.
It's called statistics.
As a sociology major we study them all the time and statistically anything is possible.
In an average snow storm over a sextrigintillion snowflakes can fall. A sextrigintillion looks like this: 1,000,000,000,000,000,000,000,000,000,00
I'm sure you math geeks recognized it right away. In a blizzard you start getting up into the Googol class. In Buffalo NY during a three day snow storm over a googol plex of snowflakes fell. Now, once you start getting into those class of numbers, the statistically impossible becomes quiet common place. In a season, a Super Googol of snow flakes can fall. In Canada, they casually get Super Googol Plex snowflake numbers.
Statistically speaking, with numbers like that, it would become more improbable NOT to have identical snowflakes.
There you have it, real science and identical snow flakes. Tell your science teacher he's full of it.
[Super Googol looks like this: Googolgoogol and a Super Googol Plex looks like this: Googol PlexGoogol. I invented those numbers. College students my use the terms without license only to confound their professors long enough to make a clean get away or to stop a berserk computer AI bent on destroying the world. The rest of you owe me.]
(Fun fact: The planet earth weighs 13,200,000,000,000,000,000,000,000 pounds. As if they could weigh the planet, more bogus science!)