fire is derived from the Ancient Greek πυρ. My question is: how did the plosive become a fricative?
I believe pyre is also derived from πυρ; why is it that pyre didn't also undergo this "fricativisation"?
As jlawer says, English "fire" doesn't actually come from Greek pŷr. "Pyre" does, but that's a borrowing (via Latin), and it's pretty clear how it happened. Instead, English and Greek share a common ancestor (Proto-Indo-European), which split into Pre-Proto-Germanic and Proto-Hellenic (and many other branches) several thousand years ago.
One of the reconstructed Proto-Indo-European words for "fire" looked something like *peh₂-wr̥. The *h₂ was probably a velar fricative, like in "loch", but there's not a strong consensus on that part. (Compare, as Arnaud Fouret suggests in the comments, the Hittite form paḫḫur.)
In Proto-Hellenic > Ancient Greek, the *eh₂w in the middle simplified to give something like *pūr; then the
/u/ fronted to
/y/, and a bit of tone funkiness happened, giving pŷr.
In Germanic (the branch of Indo-European containing English), a process called "Grimm's Law" happened, which changed voiceless stops (p, t, k) at the beginning of words into fricatives (f, th, h).
The vowel in the middle went through some strangeness involving a collective form, but the branch that would become English eventually simplified it into something like *fuir; the ui merged into ȳ, which English then turned into ī. Spelling conventions then turned fīr into fire, and the Great Vowel Shift gave it its modern pronunciation.
English fire is not derived from Greek πυρ.
Both fire and πυρ come originally from the Proto-Indo-European root *paəwr̥.
Greek simplified the *aəw vowel sequence to /ū/, but kept the consonants.
Proto-Germanic was *fūr, similar to Greek, but all Germanic voiceless stops like *p
became homorganic fricatives like *f as part of the group of consonant changes
known as "Grimm's Law".
Modern English fire comes from Old English fȳr, which was produced by fronting the Proto-Germanic
ū to ȳ, a natural process called "Umlaut", which is very common in Germanic languages.