My long-winded commentary may be interesting or just a load of cr*p. I can' really tell anymore and won't swear to either. Read on if you don't bore easily.
I have a friend who is painful to listen sing Happy Birthday, yet has an appreciation for some very complex music. He likes traditional acoustic improvisational jazz, particularly sax players, but exhibits a disconnect between listening and performing. So I think there is first a difference between the two; everyone can listen at some level, but not everyone can perform effectively. This may be a matter of practice in most cases, but I think that if 10% of the population excel at performing, then probably 10% are incapable. 80% of us can listen and play to different levels and some get better than others.
People have 2 kinds of pitch recognition attributes, relative pitch or perfect (absolute) pitch. There are people in the world like Mozart with perfect pitch that can hear 440 cycles and know it is an A, anywhere, anytime. Most of us can identify an 'A' relative to 'D' or 'E' but cannot identify the note without a point of reference, at least not without a lot of practice. Most musicians develop that relative pitch through practice, practice, practice and subsequently improve, to where some of us get better than others and develop a better 'ear'.
But you CAN develop it, and anyone who remembers a '80s memory game called Simon can attest to it. The game played musical notes adding one at a time, faster and faster. Players competed to see who could correctly reproduce the most random notes consecutively. Playing with a group of cover band musicians could produce some interesting games, which degraded rapidly as the alcohol and various other stimulants took hold. http://en.wikipedia.org/wiki/Simon_(game)
In addition to mastering pitch recognition, musicians need to master their instrument. Any musical instrument, including voice, requires a technical proficiency that involves coordination, muscle memory, and dexterity of some sort. Singers learn to control breathing, annunciation and tone. Drummers have to learn to make all 4 limbs work independently and control the sticks and pedals. A pianist controls the dynamics of the sound with the force used to hit the keys. Guitarists learn to develop finger dexterity, strength and control in order to play effectively.
Lastly, we need to learn how to work and take care of the equipment. Keeping the instrument performing at its peak and learning to make it reproduce the sounds in our head takes a lot of practice and experience. We acquire this proficiency by playing, jamming, listening and learning, like any other skill.
That's a lot to learn and it takes time and effort, and sometimes a lifetime to master (a little like golf). A little patience, persistence and practice will go a long way and is ultimately worth the effort, as for most of us on this site, there is nothing as fun and satisfying as playing music. Okay, maybe that other fun thing, the one with a partner.
This brings to mind how I recently went to Carnegie Hall with my 'tone deaf' friend to see Sonny Rollins and my wife actually asked me how to get there. I had the punch line ready before she finished the breath to ask it. I said, "Practice, Practice, Practice". I knew I married her for a reason besides the blond hair and blue eyes, shes a strait man.
btw: after 15 years of playing golf, my putting still sucks and I still keep trying that too.
That's alright, I got my guitar
-Jimi Hendrix