I blame Star Trek. (The Original Series, of course. ST-TOS was the s-f show of my adolescence, and I imprinted on it hard. Next Gen was weak tea – Earl Grey, hot — by comparison.) The weapon of choice for Kirk and Spock and everybody else who was boldly going on the starship Enterprise was the phaser, that handy gadget that looked like a bar of soap and either stunned the target or caused him/her/it to vanish completely, dealer’s choice. (I shudder to think about the complexities of investigating murders and disappearances in the Star Trek universe, given the availability of that kind of murder weapon and body-disposal tool in one easily-concealed package. Private ownership of phasers and related weapons would have to be as illegal as hell, which would of course lead to a thriving black market in same. But those are not the stories that Star Trek was about.)
Television viewers watching Kirk and Spock subdue (and occasionally disintegrate) their adversaries needed a verb to describe the action, and since the weapon was a phaser, obviously what it did to people (and occasional things) was to phase them.
(Later on, we had Kitty Pryde of the X-Men, who phased – passed through – objects. But Star Trek was there first.)
Which was all very well, but then people started using phased as a word for all occasions, including as a misspelling of the already existing word, fazed, as in, Jane wasn’t fazed – that is, “disturbed, bothered, or embarrassed” – by the sudden reappearance of the ex-boyfriend she thought she’d left behind in Patagonia.
Both phase (as a verb) and faze came into written English in the nineteenth century, but both have older roots. Phase-the-verb traces its ancestry back through the earlier noun phase (as in phase of the moon) to the Greek verb phainein, meaning “to show, to make appear.” (That initial ph- would be a dead giveaway even if we knew nothing else.) Faze, on the other hand, has a sturdy English pedigree, going back to the mid-fifteenth-century Kentish dialect verb feeze,“to frighten, alarm, or discomfit”, and back from there to the Old English verb fesian or fysian*, “to drive away, send forth, or put to flight.”
Which brings us, by circuitous means, to my peeve of the day, which is writers saying phased when what they mean is fazed.
Don’t do that, okay? It makes the baby philologists cry.
*Consistency in spelling wasn’t a big thing in Old English. Or in Middle English. Or in Modern English, for that matter, until the printers and the lexicographers between them started standardizing things.