First, the English rule has to do with syllable structure. As Colin points out, English syllable can't begin with the consonant cluster /pt/. Any word spelled that way will be pronounced some other way.
But the sequence /pt/ can occur between syllables. So if the vowel before /pt/ is stressed (as in archeopteryx /ar.ki.'ap.tər.ɪks/), then both stops can be pronounced, each in its own syllable, as Jon Hanna has noted. That's the English rule.
Of course, both words are made using the Greek word πτέρυξ 'wing', and this word, as well as the English words feather (p -> f and t -> θ via Grimm's Law), compete, perpetual, ptomaine, symptom, and hippopotamus, all are descended from the PIE root *pet- 'to rush, fly'. The /p/ and the /t/ were both pronounced in Greek.
Finally, the English word helicopter is also transparently derived from helico- 'rotating, spiral' plus -pter- 'wing'. What's interesting about this is that helicopter is such a common word that it's been split into combining forms, but not the original ones.
In English, helicopter is divided into heli- (heliport, helipad, helitaxi, helitours, ...) and -copter (cargo copter, minicopter, jetcopter, ...), because the glue between helico- and -pter- wouldn't come off, but the glue between heli- and -copter turned out to be soluble in English phonology.