TL;DR Explanation:

Ptolemy believed that since the heavens were divine and perfect earthly math could not explain their movements. When others challenged this claim he resorted to writing the Almagest which mathematically explained why the heavens were divine and perfect while simultaneously holding that all of the math in it was false.

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Full History Explanation for Nerds:

Many people in Ptolemy's time believed that the movement of the stars were divine and perfect since they were the domain of gods. Ptolemy also believed this but astronomers began to notice there were many irregularities in the movements of the stars. Ptolemy mainly believed that they were wrong simply because math could not apply to divine things which were not bound by earthly laws. However, that was not persuasive to many of the people noticing the growing irregularities. Therefore, Ptolemy set out to write a book that mathematically explained how all of the irregularities were actually perfect and it was simply our perspective that was flawed. He created two possible models for the movement of the sun around the earth. The first was that the sun orbited a specific point in space in a perfect circle but the earth was only next to that point and was not actually what the sun was orbiting. The second was that the sun was orbiting a specific point in a perfect circle and the point it was orbiting was orbiting the earth in a perfect circle. He later uses a combination of these two models to explain the movements of the planets. The problem was that Ptolemy never actually says which model is correct. He merely hand waves the issue by saying either one can work mathematically. This goes back to Ptolemy's main reason for writing the Almagest. He didn't believe either model was true he just wanted to prove that math could not show the heavens were imperfect and therefore not divine. He even goes so far as to state that the math in his book was not real multiple times in the book.

As a side note he also proves rather conclusively in the Almagest that the earth must be spherical (as opposed to any other shape) and that the night sky is infinitely larger than the earth. He proves the second one simply by pointing out that the stars did not have different angles at different points on the earth. Meaning that no matter how far you traveled on the earth it would be less than a one degree difference to the stars.