
Callum |

Let me start by saying that I believe that the intent was for non-infused extracts to only be usable by the alchemist who created them, and that's the way I would run it in my games.
Having said that, I also agree with Dasrak that, as written, the rules surrounding this are ambiguous, and that they can perfectly reasonably be interpreted to mean that an alchemist can apply his non-infused extracts to other willing creatures, but can't hand them out for those creatures to apply to themselves. (If you don't see this as a reasonable interpretation, try asking yourself this: if - just theoretically - this was the intent, how might the rules look then? Might they not look pretty similar to the rules we have?)
Furthermore, I feel that while Dasrak has been polite and clear in his discussion of this question, others have not followed suit - being rather strident in their repeated denunciations, and imputing various motivations that don't seem to be based on what he actually said. So I would like to offer my respects to Dasrak for conducting himself in such an exemplary manner.

Quantum Steve |

I'm totally for the "If it's in my mouth, it's in my possession" argument.
Get several hirelings. Pass each of them an extract. Have your hirelings use their action to feed you their extracts. Once the extract returns to your mouth it starts working and you can benefit from it's effects.
Nova out with every one of your buff extracts on round 1 and still take all your actions.

FlamingPhenex |

An extract is “cast” by drinking it, as if imbibing a potion—the effects of an extract exactly duplicate the spell upon which its formula is based, save that the spell always affects only the drinking alchemist.
Just pointing out the specific wording that extracts, sans Infusion, only affect the Alchemist.

Rory |
I swear people. Why the hell would the infusion discovery exist if you could just stand next to people and have you extract work on them as your pour them down their throats? At most it uses up the Alchemist's turn to do so but I wouldn't say that was as much as problem since it keeps the other characters actions unused.
The same reason that the spell Imbue with Spell Ability exists. It gives others in your party the ability to cast a spell (use an extract in the case of the alchemist).
There is a lot more use to the Infusion discovery than allowing the alchemist to pour a cure light wounds extract down a party members throat. With Infusion, you can "buy" an infusion (a heap cheap Heal in a bottle anyone?) from an alchemist in town, go adventuring, and have the extract ready to be used that day. With infusion, an alchemist can give an extract to the party scout so that it can be used far away from the party, or stealthily.
I'm hitting the FAQ button for the OP as I agree it could be stated clearer.

ZanThrax |

I think there's a pretty darn high probability that it'll just get 'no reply necessary'.
I agree. But if we limit the number of FAQ requests we make that we already know are going to get 'no reply necessary', the more time they can spend on the ones that could actually benefit from developer input.

Irnk, Dead-Eye's Prodigal |

The Chirurgeon Alchemist Archetype, at second level, gets to bypass the requirement for Infuse Extract when making Cure extracts. It specifically states that these & only these bypass that requirement...
Which implies that in all other circumstances (i.e.: not a 2nd+ level Chirurgeon Alchemist), the Infuse Extract discovery is required.