Why is it called the cross-entropy of q relative to p, not p relative to q? I'm looking into the definition of cross entropy from wikipedia. https://en.wikipedia.org/wiki/Cross_entropy

Cross entropy is not symmetric, so I think for sure it shouldn't be called cross entropy between $p$ and $q$.
But why is it called the cross-entropy of the distribution $q$ relative to a distribution $p$, not $p$ relative to $q$?
Also from this wikipedia page, cross entropy $H(p,q)$ can be written as
$$H(p,q)=H(p)+D_{KL}(p||q)$$
where $D_{KL}(p||q)$ is the KL divergence of $p$ from $q$, or the relative entropy of $p$ with respect to $q$. Now it is $p$ with respect to $q$？


Wikipedia calls it $KL(P||Q)$ "the relative entropy from $Q$ to $P$", so this also could be interpreted as $P$ being the "reference distribution".
The cross-entropy can be understood as the average Huffman encoding length when the distribution is thought to be $q$ but is actually $p$, i.e. the "real thing" is $p$. So, it makes kind of sense to consider $p$ as the distribution that is the "baseline".
