In RSA, why does $p$ have to be bigger than $q$ where $n=p \times q$? In openSSL – during RSA key generation – if $q$ is bigger than $p$, they exchange them. Why is that?
There's no real difference between $p$ and $q$ in RSA. It looks like OpenSSL just has the agreement "$p$ has to be bigger than $q$" for conveniences. One of the numbers has to be bigger than the other (otherwise they would be the same number, and $p = q$ is very bad in RSA).

Just use two examples: $p = 13$ and $q = 11$. $p$ is bigger than $q$, all right. What about $p = 11$ and $q = 13$? In RSA, there is no difference between the two prime numbers, so you can exchange them at will. Both are the same prime pair for RSA, even when the two numbers for $p$ in the examples are different, and "the same prime pair" means in praxis the same key.