Why do we classify with P(class | features) instead of P(features | class)? Most of classification models are based on searching for a class maximizing P(class | features). But why not the opposite, P(features | class)?
Then, the second question is, are there any situations where the latter is more appropriate?

We do classify with P(features | class).  Recall from Bayes rule...
$$ P(y \vert x ) \propto P(x \vert y) P(y) $$
with equality if we divide by a normalizing constant.  P(features | class) is a part of P(class | features)
