Why is the Englishman Santiago's foil in The Alchemist?

Great question! To fully answer your query about the Englishman in Paulo Coelho’s novel The Alchemist, it is important to fully understand the concept of a foil.
In literature, a foil is a character who mirrors another character, most frequently the protagonist. A foil is similar enough to the protagonist for a reader to see parallels between the two. For example, both may have the same motivations, the same background, or the same personality. However, a foil differs from the protagonist in some major way that creates a visible contrast. This contrast between characters highlights certain qualities of the protagonist. In Coelho’s book The Alchemist, the Englishman fits this mold of a literary foil. To clearly explain why, we need to review the characteristics of the protagonist.
The protagonist of The Alchemist is Santiago, a youthful Andalusian shepherd. Santiago journeys to the Egyptian pyramids in search of a treasure. However, Santiago’s journey quickly shifts purpose when he meets the elderly King Melchizedek, who reveals that he helps all those who seek their Personal Legend. Santiago is provided with magical stones to help him on his journey, and his voyage to Africa becomes a journey of spiritual self-discovery.
Santiago is curious and marvels at the wonders of the desert around him. He is open-minded and trusting of others. This is evident in how willing he is to abandon his home in search of his destiny. Santiago is also an extrovert and actively converses with everyone he meets. When Santiago first meets the Englishman, the similarities between the two characters are striking. As the plot unfolds, the differences that make the Englishman a foil to Santiago become increasingly apparent.
The Englishman, like Santiago, is also on a journey to find his Personal Legend. He possesses his own set of Urim and Thummim and accepts the omens. However, unlike Santiago, the Englishman is a man of science who devours books and prioritizes knowledge over experience. For example, the Englishman is oblivious to the beauty of the desert and has no sense of wonder.

When the people saw that star shining in the morning sky, they knew they were on the right course toward water, palm trees, shelter, and other people. It was only the Englishman who was unaware of all this; he was, for the most part, immersed in reading his books.

The Englishman is so immersed in books that he doesn’t notice the beautiful world around him.
His prioritization of book-learning also tempts the Englishman into intellectual arrogance and pride. For example, examine the Englishman’s perspective on Santiago after he fails to learn much from his books.

The Englishman was disappointed. The years of research, the magic symbols, the strange words and the laboratory equipment . . . none of this had made an impression on the boy. His soul must be too primitive to understand those things, he thought. He took back his books and packed them away again in their bags.

The Englishman’s intellectual arrogance is a handicap in his quest for a Personal Legend because he cannot learn from others.
The Englishman is also less apt to trust and learn from the people around him. His distrust of the other caravan-members is best exemplified when Santiago learns that the Englishman has been carrying a revolver. The Englishman says that the revolver “helped me to trust in people.” This statement shows just how wary the Englishman is of others and contrasts starkly with the trusting attitude of Santiago.
The Englishman in The Alchemist is a clear foil to Santiago. In many ways, the two characters are similar, as they both seek their Personal Legends and travel in the same caravan. Despite his similarities with Santiago, the Englishman’s intellectual pride, distrust of others, and inability to learn from experience make him a clear foil to the protagonist. Santiago’s positive qualities of trust, openness, and appreciation of beauty are highlighted and emphasized by the Englishman’s presence.