tell the reason why the author ended with that closing scene

This analysis comes straight from gradesavers study guide for Canterbury Tales. It has everything you could possibly need to answer the question you've posed here.

One of the biggest questions about the Tales as a whole is precisely how they end. Throughout his works, and even within the Tales (look, for example, at the interruptions of Sir Thopas and the Monk’s tales) Chaucer proves that he knows how to create a false ending, a trick ending, which ends by not ending, by not concluding. The Canterbury Tales ends on a decidedly pious and religious note, first with the Parson’s lengthy sermon, and then with a retraction written as “Chaucer”. The Parson’s sermon, a translation from a medieval work designed to advise clergy in the salvation of souls, would be a plausible medieval sermon – there seems nothing in it that is ironic: it is a perfect example of its genre.

Yet can the Parson’s sermon seem anything other than just another genre? In a work which has anthologized genres – we have already read beast fables, saint’s lives, fabliaux, Breton lays, and all manner of other stories – and problematised them, drawing attention to their speaker’s voice as something (as the Pardoner points out) ventriloquized, can we really be expected to take the Parson’s voice seriously?

Critics disagree wildly about the answer to this question. The same problem applies to Chaucer’s retraction – which, as in the Man of Law’s prologue, blurs the line between the Chaucer writing the Tales (who has also written the Book of the Duchess, Troilus and Criseyde, and so on) and the fictional Chaucer who is a character within the pilgrimage. Is the Chaucer who writes these tales just another constructed voice?

Or, perhaps, is the Retraction of the tales a genuine one? Chaucer, in this theory, genuinely was dying and was unable to finish the work – or for some reason, felt the need to immediately retract it, as he genuinely believed that it did come too close to sin. Thus, before the Host’s plan was complete, he concluded the tale with a pious sermon and then a Retraction: no-one could therefore accuse the Tales of being unchristian. Is it a death-bed confession?

A Retraction is a fairly usual way for a medieval work to end, and perhaps that points us to the aforementioned effect: its very normality is perhaps a clue that Chaucer’s intention is not pure and simple. For it could be read simply as another “funny voice” – the voice of the Chaucer who told Sir Thopas: could be read as comedy rather than penance. Moreover, as E.T. Donaldson has firmly stated, the use of the Parson’s Tale as an interpretative key to unlock the whole of the Tales is problematic, particularly when you consider the deliberate religious provocation of tales like the Miller’s, the Wife of Bath’s and the Merchant’s. The tales by no means seem to be written to a purely Christian agenda - though Christianity is undoubtedly a key theme.

End-points in Chaucer are difficult to definitively interpret, and perhaps this dichotomy was intended by Chaucer himself. Perhaps this ending is simply one way of closing down the Tales – the Manciple’s tale, of course, has been only the most recent in a line of tales which reiterate the advice of these final fragments to hold one’s peace, and know when to fall silent. Is this Chaucer, on an imaginary, real or literary deathbed, punningly, holding his peace, but also being “at peace”? One thing is for sure: understanding the ending of the Tales seems a fitting encapsulation of the complex problem of interpreting the work as a whole.