Jack Lewis declared himself to be a very typical middle Anglican, not high or low.
He was against RCC teachings, because of his childhood in Ulster.

The Anglican Church around the world has Thirty-Nine Articles of faith.
Here is a page from the [Anglican] Church of Ireland:
https://www.ireland.anglican.org/our-faith/39-articles-of-religion

Number 28 includes a statement about Transubstantiation. It's worth reading in context.
Number 22 speaks about Purgatory.

(Personally I don't think he really believed in Purgatory, but I do like his idea of there being a 'mouthwash' after the 'tooth of life' is pulled. )

I use to think that he didn't believe in Purgatory either. I will try to find the link. Also, Lewis prayed for the dead. How do you call that low or high Anglican?
Yes, I've read the thirty-nine articles many times. Like, I said I will post the links on here, to where I heard those claims.
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Coracle, I never said held the Roman Catholic understanding of Purgatory. Check out the following links, I'm here interested to here your take.
https://churchpop.com/2017/05/06/why-th ... purgatory/
“Our souls demand purgatory, don’t they?” Lewis asked in Letters to Malcolm: Chiefly on Prayer.
https://www.baptiststandard.com/news/fa ... vens-sake/
Like I said, one of these links claims Lewis distinguished Dante's understanding of Purgatory, from that of the Catholic Church. That said, Lewis still believed in it. He clearly says so in Letters to Malcolm.
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While Lewis was not Roman Catholic, according to Wikipedia, he is often considered Anglo-Catholic.
I have demonstrated that Lewis believed in Purgatory, though I don't fully understand how he saw it. But back to topic, why did Lewis reject Transubstantation?
To me, Lewis was clearly a high church anglican, with an evangelical touch.

Why does any Protestant reject Roman Catholic teaching? Answer that question and I think you’ll come to understand why Lewis’ theology sometimes differs with Roman Catholicism and sometimes coincides with it.

I'm a Protestant, but it's besides the point why Lewis was a Protestant. My point is simply that Lewis held close to Roman Catholicism on a few points, so simply saying he's a Protestant and that's why he rejected Transubstantiation doesn't answer my question.
Also Protestants have many reasons for rejecting Roman Catholic theology, for some it's because of Scripture Alone, for other's it is not. Some Protestants are not Catholic because of the papacy, for others it is justification or the Marian doctrines. Protestants can have all sorts of reasons why they are not Catholic, some more than others.
To many evangelicals, a Lutheran would be seen as too close to Catholicism. Do you see my point? Asking why Protestants aren't Catholic does not answer why Lewis rejected this doctrine.
Most historians consider Henry VIII as starting The Church of England {though some say Elizabeth I}. If the first is true, and one considers Henry VIII Protestant, that would be also important to remember as he believed in Transubstantiation despite the fact that over time he departed from Roman Catholic theology on other areas. Further some Anglo-Catholics, {though they would not consider themselves Protestants} usually speaking believe in Transubstantiation. The Six Articles of The Church of England, which was written prior to the later thirty-nine articles, further taught it.

I think what Stylemetro meant, Jewel, is that it can be hard to say why any particular person doesn't believe a particular thing. Some people spend more time explaining why they believe things than why they disbelieve things. It's possible Lewis wrote somewhere why he didn't believe in the transubstantiation but it's also possible he never felt the need to defend this particular nonbelief.

But don't you wish you knew why he rejected it? I'm fascinated by Lewis's theology!

Maybe he rejected it because it wasn’t “mere Christian” enough for him. I think Lewis considered himself more so your average follower of Christ not overly theological in his thinking. He kept things simple. I think you can see that in the Narnia stories. There are Christian elements, but those elements don’t scream out ‘this theology’ or ‘that theology’. Sure, one can interpret his rendering of Aslan as ‘this’, and the White Which’s actions as ‘that’, but it’s only speculation. I think he was probably okay with it all being speculation. He knew Jesus was the Christ. How that works for certain, he was only willing to speculate. That’s my take anyway.

Jewel, if Lewis considered himself a typical average Anglican (not High, not Anglo-Catholic) then he would follow what the 39 articles say.
The English Reformation (when not fussing about Henry VIII's marriage and succession problems) looked seriously at the teachings of scripture in forming its doctrinal statements.

This particular issue is a very important one for Protestantism.
I see no reason to show disrespect to Lewis, who explained that he was an average Anglican, and that his childhood in Northern Ireland had a strong influence on his not accepting RC doctrines.

I'm not very familiar with all of Lewis's personal theological beliefs — he doesn't say anything about transubstantiation specifically in any of his works that I've read, anyway (which isn't that many) — but this is part of what Wikipedia has to say about Anglicanism and transubstantiation (emphasis added):

Transubstantiation — Anglicanism

Official writings of the churches of the Anglican Communion have consistently affirmed Real Presence of Christ in the Eucharist, a term that includes a belief in the corporeal presence, the sacramental union, as well as several other eucharistic theologies.

Elizabeth I, as part of the Elizabethan Religious Settlement, gave royal assent to the Thirty-Nine Articles of Religion, which sought to distinguish Anglican from Roman Church doctrine. The Articles declared that "Transubstantiation (or the change of the substance of Bread and Wine) in the Supper of the Lord, cannot be proved by holy Writ; but is repugnant to the plain words of Scripture, overthroweth the nature of a Sacrament, and hath given occasion to many superstitions." The Elizabethan Settlement accepted the Real Presence of Christ in the Sacrament, but refused to define it, preferring to leave it a mystery. Indeed, for many years it was illegal in Britain to hold public office whilst believing in transubstantiation, as under the Test Act of 1673.... In the Church of England today, clergy are required to assent that the 39 Articles have borne witness to the Christian faith.

There's more in the link above, but it seems the standard Anglican position is that Christ is truly present in the sacrament, but the bread and wine don't literally, physically become the body and blood of Christ. Given that, it doesn't surprise me that Lewis rejected belief in transubstantiation and apparently didn't feel any need to explain why in detail.

Courtenay: It appears the Anglican position is that it is a mystery, but definitely not THAT mystery.

Actually, the more I think about this topic, I don’t see a lot of emphasis of the thanksgiving meal in Lewis’ stories. He seemed to prefer analogies of the Lion of Judah and even the Lamb of God. But not so much the Bread of Life. I could be wrong about that, and if so, perhaps someone can show me examples of his in this regard.

For example, his contemporary JRR Tolkien, who was Catholic, used the concept of the Lembas bread in his Middle Earth stories which was a bread that was substantial in it’s properties as food for the journey.

To answer Jewel's question about Lewis' theology...not really. Lewis' main claim to fame was being an apologist (and of course an author ) rather than being a theologian. A number of the concepts he believed in, like limbo and inclusivism, I consider to be "bunk" to use an old fashioned term.

He did have quite the way with words though and if he left any quote about why believed or disbelieved in transubstantiation, I'm sure it'd be entertaining.

As an Anglican myself, one who usually worships in "Low Anglican" or "Evangelical Anglican" churches, my own position is that the elements do not change, but are given a special blessing, a holiness (holy = set aside, rather than being special in itself), through the prayer of thanksgiving said during the service. They remain bread and wine but are now special, because of what they represent.

There are many Anglicans who may be called "High Anglican", and prefer a more formal ritual (in England particularly, but also some in other countries). People of my parents' generation would still give a little bow as they go forward to receive the elements; I can't state what this indicates about their understanding of the issue.

Perhaps we Christians tend to assume that Lewis thought as we do?

...There are many Anglicans who may be called "High Anglican", and prefer a more formal ritual (in England particularly, but also some in other countries). People of my parents' generation would still give a little bow as they go forward to receive the elements; I can't state what this indicates about their understanding?...

I find this information very interesting as someone who also bows as I receive Holy Communion. For those who do not know on these forums, I believe in Transubstantiation.

Thanks for sharing.