Why is "fastly" not a word?

As well as being an adjective, fast is an adverb. We use it all the time as such:

He ran fast.

However, though slow is definitely an adjective, it sounds wrong when used as an adverb, because slowly is more common.

He ran slow.

We would always say:

He ran slowly.

My question is, why isn't fast treated the same way as slow; why is there no fastly, while there is a slowly?

Because real, living languages have quirks and are never entirely systematic. The "ly" ending is generally indicative of an adverb in English, but not all adverbs end in "ly", and not all words ending in "ly" are adverbs.

Absolute consistency in a language is an indication that the language is a pidgin, a relatively new creole, or an artificial language (like Esperanto or Volapük). Any language that is in everyday use and has been around long enough to gather scratches and dings, will have them.

Quick and fast are both words that may or may not be related to rapidity. In their adjective forms, quick also means living, and fast can mean secure or firm. As an adjective or an adverb having to do with speed, fast seems to have been the result of some strange semantic drift in the period leading up to Middle English.

From etymonline:

fastly `(adv.): "quickly," c.1200, former adverbial cousin to fast (adj.), from Old English fæstlic "firmly, fixedly, steadfastly, resolutely;" obsolete in 19c., simple fast taking its place.

So it was in fact a word, but has fallen out of use.