Word or phrase for "seeing meaning where none exists"

Is there a word or a phrase to describe an instance where meaning is ascribed to something where there is no such meaning or where the interpretation is particularly fanciful?

For example, when reading Shakespeare in English class or when viewing modern visual art in Art Appreciation class, someone mentions the 'phallic imagery or symbolism' of anything cylindrical in what is being read or viewed.

It's a phrase, not a word, but there's the expression reading too much into something, as in:

Matt, I think you're reading too much into it.

TFD lists read into as a phrasal verb, meaning:

to attach or attribute a new or different meaning to something; to presume inferences as one reads something.

That seems to be pretty close to what you're after.

Pareidoilia is seeing meaning in random stimulus, such as seeing faces or animals in cloud patterns.