I think that the GM may be conflating the alchemist's fire (flask) with a magic potion's Physical Description that, in part, says, "A typical potion or oil consists of 1 ounce of liquid held in a ceramic or glass vial fitted with a tight stopper. The stoppered container is usually no more than 1 inch wide and 2 inches high." The typical vial for ink and potions, by the way, has negligible weight. Potions, it should also be noted, typically have no relationship to items created using the skill Craft (alchemy).
There can still be controversy, though, if you want it. For convenience, Pathfinder likes to measure in pounds whenever it can, using cubic feet when it must and liquid measures only by necessity. This makes computing the flask's volume from its listed weight problematic. That is, the rules say that an alchemist's fire (flask) weighs 1 lb., and that's all the game really says about what could possibly be a flask of alchemist's fire's volume. As per Weapons on Weapon Size, a reader could assume that an alchemist's fire flask is either a light weapon or a 1-handed weapon for the purposes of throwing while two-weapon fighting. That makes an alchemist's fire flask's equivalent creature size category either Small (therefore 2-4 ft.) or Diminutive (therefore 1–2 ft.), but those seem awfully big to this reader, and size categories are approximations anyway. (N.b. This GM rules that flasks of alchemist's fire and similar items are closer to darts and shuriken than to nets and javelins so in his campaigns things like this are light weapons, but ask your GM.)
And with this in mind it becomes possible for a GM to go to the extreme edge of all these rules and say that an alchemist's fire (flask) is a 4-ft.-tall flask that weighs 15 oz. and that contains "a mix of several volatile liquids that ignite when exposed to air" that weighs but 1 oz. This player—who, to be fair, is not well-versed in fluid mechanics, glassblowing, nor alchemy—wouldn't flip the table and storm out of the campaign of a GM who made such a ruling, but this player would find such a ruling severely stretching his limited imagination—especially if his PC had been until this point—somehow!—carrying on his person and within easy reach 10 or so of these unwieldy-yet-still-1-lb. flasks of alchemist's fire. (Although not within so easy reach as to be able to be drawn quickly… sigh.) Further, bear in mind that cumbersome flasks like these would be, for example, (ahem) largely impossible to conceal using the skill Sleight of Hand as the GM's ruled they're Small objects.
All that said, because this player and GM isn't a scientist, he has always imagined—and played—that the alchemist's fire (flask) and similar items are closest to a hip flask (rather than, for example, a laboratory flask), and those—Amazon.com tells me—tend to average a capacity of 8 oz., making it so that—in this GM's settings, anyway—the typical 1-lb. flask weighs 0.5 lbs. and its contents 0.5 lbs. (Of course, that ruling's not because that's an accurate assessment of the weight/volume mismatch that's occurring here but because that ruling's playable and convenient; likewise, this convenience extends to matching the official statistics of the hip flask rather than the more massive 3-cp, 1.5-lbs.-when-it's-empty, full-on I-don't-even flask (empty) that Pathfinder inherited from D&D 3.5e that I imagine is about as subtle as this.)
However, unless the argument is really about whether or not an alchemist's fire (flask) can be hidden using the skill Sleight of Hand, according to the rules, the alchemist's fire (flask) always breaks when deliberately thrown, never breaks when it's not deliberately thrown, and can't be opened without its contents igniting in contact with the air. Thus, unless the GM rules otherwise (or PCs concoct a dangerously wacky plan!), the contents of an alchemist's fire (flask) can't be, like, decanted into a barrel suitable for use as special siege weapon ammunition (such ammunition must be specially made) or for rolling at enemies or to decorate a secret base in hopes that errant attacks from firearms against them will kill intruders, so determining its volume is typically unnecessary.