A person can learn to play the guitar without a formal music instructor. This is not to say that it would not be helpful to have formal lessons, as it obviously help anyone to get a good, sound foundation in the learning process.
The facts are, however, that the majority of people who learn the guitar, learn on their own with a chord book, and the painful toughening up of their fingers on the wire strings.
Many will learn chords to their favorite songs and learn chord sequences the same way. For example, many songs are played in C, F, G or D, and corresponding chords are learned while the song plays on the MP3 or similar venues.
A song based in C would also have Am, F and G as chords in the progression in a 4/4 time song. The same is true for other songs that can be learned in the same way.
A person can learn many songs in this manner and also be able to learn individual notes and basic instrumental runs, that are taken from the chord progressions.
Having said all of that, learning guitar on your own is easy if you follow these steps, if you have the extra expense covered, hiring a qualified tutor, teacher or coach, however you wish to call such a person, you will progress much faster in your quest to learn guitar.
For one thing, you will learn to read music, which you will probably not learn on your own, and you will learn how to read tabs, which you will not learn on your own either. Both are extremely valuable if you ever wish to play professionally or take up the instrument in a more detailed manner.
You will also learn much more about chords and the proper way to play them, and all of their combinations, which is really the essence of guitar playing.