Actually, the Ancient Mariner is driven to tell his story to almost anyone who will listen. He chose the wedding guest because, for whatever reason of his own, the wedding guest couldn't help but listen:
It is an ancient Mariner,
And he stoppeth one of three.
`By thy long beard and glittering eye,
Now wherefore stopp'st thou me ?
The Bridegroom's doors are opened wide,
And I am next of kin ;
The guests are met, the feast is set :
May'st hear the merry din.'
He holds him with his skinny hand,
`There was a ship,' quoth he.
`Hold off ! unhand me, grey-beard loon !'
Eftsoons his hand dropt he.
He holds him with his glittering eye--
The Wedding-Guest stood still,
And listens like a three years' child :
The Mariner hath his will.
The Wedding-Guest sat on a stone :
He cannot choose but hear ;
And thus spake on that ancient man,
The bright-eyed Mariner.
That's it: at this point the wedding guest is spell-bound and the Mariner begins his tale.
Maybe it should asked, Why, of all people, is a wedding guest, in general, chosen? Well, in some ways the tale that is told by the Mariner has the sense of a wedding about it. The Mariner becomes, after much travail, wedded to a new way of thinking about and loving life and the other creatures of the earth.
At first he felt a separation between himself and the albatross and all the "slimy things" that "did crawl with legs Upon the slimy sea." But at last he learned a deep truth:
He prayeth well, who loveth well
Both man and bird and beast.
He prayeth best, who loveth best
All things both great and small ;
For the dear God who loveth us,
He made and loveth all.
What a fitting little sermon for the Mariner and the wedding guest who both missed the more traditional wedding.
The Ancient Mariner just has a way of sensing to whom he must tell his tale next. The exact reason for his choosing of the wedding guest is not clearly stated, other than that the mariner knows to whom he must relate the story of his experiences just by seeing him. Near the end of the poem, in lines 583-587, the mariner explains,
"I pass, like night, from land to land,
I have strange power of speech;
That moment that his face I see,
I know the man that must hear me:
To him my tale I teach."
The Mariner has committed the sin of killing the albatross, and as a sort of penance for his transgression he must wander the world telling his tale; if he does not do this, he is tormented "with a woeful agony" (576). When he has found the right listener, however, and related his experience, he is then set free from his guilt for a time. The Mariner's tale has a moral, which is,
"He prayeth best, who loveth best
All things both great and small;
For the dear God who loveth us
He made and loveth all" (611-614).
Apparently, the wedding guest chosen by the Mariner has a need to hear this message. Something in his life is amiss, and by hearing the Mariner's story, he becomes a better person, albeit "a sadder and a wiser man" (621).
Coleridge wanted his poem to be spoken by a fictitious narrator in order to avoid giving the impression that he was speaking about an experience of his own. He invented the ancient mariner for this purpose. The fact that this eccentric character seems so authentic adds to the verisimilitude of the long tale. He is exactly the sort of person who could have had that sort of strange experience.
Coleridge also felt obliged to invent another character to whom the ancient mariner was telling his story, although he probably could have claimed that the story had been told to him personally. By having the ancient mariner insisting on telling his story to the wedding guest right in the here and now, especially with the wedding ceremony imminent, a sense of immediacy is created which would have been absent if Coleridge simply claimed that he was repeating a story told to him at some time in the past.
Coleridge added drama to his tale by creating conflict between the ancient mariner and the wedding guest. The wedding guest is late for a wedding, and apparently he is someone who is of importance to the ceremony. He does not want to stop and listen to the weird old character's story and keeps protesting that he is late. But the ancient mariner has "strange power of speech" and holds the younger man against his will.
This is a clever way of adding drama to the poem by creating conflict, which is the essence of drama. Part of the conflict is due to what is called a "ticking clock," a time factor that gives a sense of urgency. The wedding guest does not merely want to evade this seedy-looking old vagabond (who may be planning to ask for a handout), but he has a pressing engagement which increases his motivation to get away from him.
The poem about the actual voyage is a story within a story. The cover story ends with the wedding guest being allowed to go on his way, a sadder but a wiser man.