I'm going through the course right now, and the instructor is saying some strange things, clearly (to me) ignoring that what he's saying is only true in very specific contexts.

For example, in the video I just watched he said "the natural way to compute the distance between two vectors is using cross entropy." And then he goes on to describe some unnatural features of cross entropy. The truly "natural" way to compute distances between vectors is the Euclidean distance, or at least any measure that has the properties of a metric.

I can understand this is a crash course and there isn't time to cover nuances, but I'd much rather the instructor say things like "one common/popular way to do X is..." rather than making blanket and misleading statements. Or else how can I trust his claims about deep learning?