Err... I must seriously disagree that absolute pitch cannot be learned. It can be learned and if it can be learned then it can be taught!
Absolute pitch is the ability to identify different pitches - the vibrations in the air.
But most people do not think in terms of the different rates of vibrations they hear; they think in terms of musical material. As such, Happy Birthday sang using a pitch most comfortable to one person's voice can be sung by all - relative pitch - with no conscious regard that they started on Bb or C. However, when someone pays attention to given vibrations and is then able to consciously realizes them and identify them, we have what is called perfect pitch.
Why do some people have this ability and others do not? Maybe it's wired into the brains to consciously identify these different rates of vibrations primarily and musical content afterwards but this abilty is also conditional.
There are prerequisites to this ability: the most important is that pitches are absolute - that is, no exposure to flexible pitches. Pitches must vibrate at a non-changing Hz (for example A above middle C = 440Hz). If not, then having perfect pitch would be impossible and it wouldn't matter anyway and if it doesn't matter, this ability would have no need.
So if Absolute pitch is an ability that is acquired consciously, why doesn't everyone acquire it? It depends on how people's brains assimilate information. Do they consciously think of pitches or do they think of musical content? Are they an instrumentalist where the pitches are fixed according to their instrument? Let's examine the piano.
The piano is a fixed pitch instrument. When you want to play middle C, you are
not required to think how it sounds like, all you have to do is visually identify it by the relationship of the black and white keys and the middle of the keyboard. Just depress this white key at a given velocity and voila!... I speak French! In fact, the keyboard is perhaps the least helpful for developing this skill because playing the keyboad is primarily learned visually, then tactilely. It wouldn't matter if you know how it sounds like before you play it if you don't know the associations between sound and keyboard geography. (In fact, this also has interesting aspects which I'll discuss later.)
So you see, even though the piano is a fixed pitch instrument, most pianists never acquire this ability because they are not aurally conscious of it. They are primarily visually and tactilely oriented with the piano which has led to this joke: There are musicians and then there are conductors and pianists - neither have to listen as they perform.
Different kinds of Perfect Pitch associations---------------------------------------------
So what about the associations of sound and keyboard geography? What if you know how a piece sounds like right before you play it? What if you have practiced a piece so well that it's in your aural mind and fingers? If this is true, then you'd never play a wrong note and you'd never make a mistake and forget where you are in the piece. This is aural memory associated with muscle memory. If your muscles recieve a different sensation than the one you are practiced to, then you make a mistake and suddenly, you have no idea where you are in the piece and where to put your fingers. To prevent this from ever happening is this: consciously have your aural memory associated with keyboard geography. Once this is learned, you'll be able to improvise in your mind and be able to perform it in real time (assuming your mind isn't improvising physically virtuosic music you can't actually play.

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Once you've acquired this association, you can simply show this skill to others: When you hear a pitch, you associate it with the keyboard and identify the note based on what key you have to play to make that sounds.
Another association is simply to associate letter names with the given pitches. You hear 440 vibrations per second, you associate it with the letter 'A' and so forth. This is aural association with naming association, much like associating a name to a face - everyone can do it. This is why those without perfect pitch can learn it when they are taught sight-singing using fixed "do" as opposed to movebale "do" - they have associated certain pitches with sylables (names). This may also explain why some with perfect pitch have a very difficult time identifying pitches when they are sung by classical singers - the sylabic/vowel combinations are too vast to clearly identify and are confusing especially when they open up their afterburners and vibrato kicks in.

But I'm digressing.
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Absolute pitch can be developed - it's just not necessary for most people to do so and their instruments can also be of hindrance to developing it. Developing this skill means consciously making different associations than the one you already have. It's difficult to sew on another arm when the two you have work just fine but imagine the benefits to a pianist - 3 hands!