Why is bayes theorem formula always presented in the hard-to-remember way? $P(B|A)\cdot P(A) = P(A|B)\cdot P(B)$
would be so much more intuitive to understand and thus easier to remember.

You have the tag "Bayesian", so I just thought I'd mention the centrality of the posterior distribution $P(B|A)$ (where $B$ is an unknown parameter and $A$ the data) to Bayesian inference.
In other words, it's because $P(B|A)$ tends to be the thing we care about.
