There are many wrong-headed elements to that, so it's hard to know where to begin, other than to say "Oh yeah, it's rubbish," but I have a guess as to where your teacher is getting these ideas from.

I suppose one must acknowledge that, given the amount of Arthurian tales floating around, it's likely that at some point or another some parish priest used Arthur in a homily for illustrative purposes. Perhaps some reference is extant, but if so, I'm unfamiliar with it.

And, I suppose one must acknowledge that the eventual development of Arthur as the once and future king has often been seen as Christ typology, and I think that it's fair to see certain depictions of him in that way ... indeed, I certainly do.

I'll let others deal with the idea that the Church "kept folks out via requiring them to speak in [L]atin" at length, except to say that it's a bizarre inversion of the role of Latin in the medieval church. Latin acted as a unifying force, allowing the Church to communicate with itself across cultural lines. Even if we want to say it was part of an insidious agenda to keep people out of the Church (an odd strategy for church growth and evangelism), lots of people in the Church had poor Latin and were illiterate even in their native tongue, so it certainly didn't keep people out if that was its intent.

Instead of focusing on that, though, I'd like to look at the rest of the claim, that the Church created Arthurian legends to teach people about Christ. The origins of Arthurian legend are notoriously difficult to pin down, and in fact it's likely that different legends have different sources. Many were likely pre-Christian sources.

So, instead, let's take the best possible view of your teacher's claim, and look at Geoffrey of Monmouth's Historian Regum Britanniae, which you can find in free pdf here, though if that translation's not to your liking, there are many, many more. Now, while we've got some earlier written references to King Arthur (such as Nennius's Historia Brittonum), they tend not to be tales, but are references. Now, at the same time, we've also got these bardic traditions of Arthur growing up, and those are narratives that we would call "tales" proper, those aren't really associated with the Church. So, I think Geoffrey of Monmouth's History of the Kings of Britain would probably be the best place to start, since it also tends the be source for much of what follows.

At first glance, it might appear that Geoffrey's work bolster's your teacher's claim. It was written in the 12th century, so definitely was not pre-Christian, and Geoffrey of Monmouth himself appears to have been a cleric who held various positions in the Church. So, here we have it, a Christian cleric who wrote influential Arthurian legends!

But here's why that doesn't work: First, he wrote in Latin, so that kind of blows out of the water the idea that it was intended to teach about Christ to non-Latin speakers.

Second, though, let's forget that it was written in Latin and actually read the book itself. The book is pretty long, and we don't get to Arthur until far into it, but it's still a really fun and interesting read, so I'd strongly encourage you to read the whole thing. Once you read it, I think you'd be hard-pressed to see Arthur in that as a Christ figure. If anything, he's more the return of Constantine, with Britain being the second coming of the City of Troy. Indeed, the tone of the whole book seems to be "look at the glorious history of the Britons, and how we had really great kings long before the coming of the Anglo-Saxons," rather than a Narnia-esque allegory for Christ.

You particularly mentioned Sir Gawain and the Green Knight, though, so let's have a look at that. Remember what I said about Geoffrey seemingly showing Arthur as the second coming of the city of Troy, rather than of Christ? Well, SGGK explictly makes the Trojan connection in the very opening line! Arthur himself is basically a side character, and its hard to see how he could be seen as a Christ figure in the poem. Sir Gawain himself, with his comic near-seduction and his embarrassing confrontation with the Green Knight in the end would seem to be a very odd Christ. Maybe, maybe we could argue that the Green Knight himself is a Christ figure (since he appears mysteriously, is struck down with a death blow but lives, etc) could be a Christ figure, but since he's more-or-less the villain (and working for Morgan le Fay), he also would be a weird Christ.

So, where might your teacher be getting this from? Well, the Gawain poet is credited with three other texts (all found in the same manuscript), and these definitely are for Christian didactic purposes. Patience and Cleanness are poetic homilies, so they're not great examples, but The Pearl(found here in a Modern English translation linked to a Middle English translation) really is an example of what your teacher is talking about, I think. It's a dream vision about the Pearl of Great Price parable found in Matthew 13:45-46, and although the Pearl is really the Kingdom of Heaven, not exactly Christ, it is a narrative poem illustrating one of Christ's teachings. OK, so the Gawain poet didn't exactly invent Arthurian legends, nor does he appear to be using SGGK to teach about Christ, but he did elsewhere write in a tale in English about one of Christ's parables. Not exactly the claim, but almost sort-of close to it.

Here's my guess as to where your teacher is coming from: Perhaps he is trying to read Sir Gawain and the Green Knight in the context of the Gawain Poet's other works, and so is conflating it with The Pearl, and then draws from that broad conclusions about the Church and its role in the origins of Arthurian legends.

I think your teacher's claims as you've presented them here are rubbish, but my advice would be, rather than trying to correct your teacher, to read those texts I've linked to here, and see what's true for yourself.