In Toy Story 2, Andy's Buzz Lightyear removes the New Buzz Lightyear's helmet (from the toy store) to prove to his friends that He is the Andy's Toy Buzz. Why was the Buzz from the Toy Store not able to breathe normally?
2 Answers
Similarly to Andy's Buzz, this new Buzz also doesn't know that he is a toy. So, when Andy's Buzz removes the helmet from the new Buzz's head, he thinks that he can't survive in this unknown environment without the suit's air supply, which is due to psychological thinking. This same thing happened to Andy's Buzz in Toy Story 1.
In Universe
The fact that he could breathe just moments later after the old-Buzz got him to calm down for a moment proves that he could breathe normally. It was a purely psychosomatic reaction based on Buzz's (both of them) initial belief that they really are Space Rangers.
Slightly Out Of Universe
This gag mirrors Old-Buzz's reaction when Woody attempts to get him to understand the truth about being a toy in the original Toy Story movie.