I believe that many people write you’re as your because they pronounce you’re in the same way that they pronounce your.

Given that they always hear your, they always write your.

I saw this on a T-shirt.

Problems:
1. “THATS” is missing an apostrophe.
2. “YOUR” is not the correct word.

Explanations:
1. The full sentence is “That is hot.” The contraction of “That is” eliminates the space and the “i” and requires an apostrophe to indicate the contraction.
2. The full sentence is “You are not.” The contraction of “You are” eliminates the space and the “a” and requires an apostrophe to indicate the contraction.

Solution:
“THAT’S HOT / YOU’RE NOT”