Douglas Harper's Etymology Dictionary
hot-rodders' slang, 1952, perhaps from peel "blade or wash of an oar" (1875, American English), earlier "shovel-shaped instrument" (see peel (n.2). Or it might be from aircraft pilot phrase peel off "veer away from formation" (World War II), or from earlier American English slang peel it "run away at full speed" (1860).
Wiktionary
vb. (context idiomatic US automotive English) To start abruptly from a standing stop, accelerating rapidly, especially so as to produce skid marks.
Usage examples of "peel out".
The girl spit what was left of the lemon peel out on the floor, further disarranged her hair by running her fingers through it, wiped her mouth with the back of her hand, and slapped the table.
Put old fruit or peel out and possie might eat them and leave your fruit alone.
She lay on the bed and watched him peel out of his jacket, then remove the shoulder holster, which once more carried its lethal cargo.
His brain felt like the engine in the biggest fucking Chrysler ever built, idling on fat gas, waiting for him to drop the car into gear and peel out.
He could peel out of the coveralls and the stimsuit, shower in the public gym, dress himself in stationer style and go down past helldeck to 1, where he weighed Earth-normal, walking like an old man, it might be, but he’.
He'd started to peel out of his jacket, and now he drew it off slowly.
Switch on your headlights and drive all the way down to the fence, turn around, and peel out of the lot.
His armor legs seized up, and he lay wriggling like a frantic fish in an effort to peel out of it.
Another two clicks, and I saw Skeeter up above me peel out of marshal and head east.