Final answer:
Henry initially liked Anne Boleyn for her potential to provide a male heir, her intelligence, and possibly her Protestant sympathies, but when she did not produce a son, she was executed after being accused of adultery.
Step-by-step explanation:
Henry VIII favored Anne Boleyn because he believed she could provide him with the male heir he desired for the Tudor monarchy. Impressed by her intelligence and allure, Henry was also motivated by the potential for a male succession to secure the throne and his legacy.
The Act of Supremacy in 1534, which essentially created the Church of England and allowed Henry to annul his marriage to Catherine of Aragon, points to the lengths Henry went to marry Anne. However, Anne was unable to provide a male heir and was executed following accusations of adultery.
The religious aspect, where Anne may have secretly held Protestant sympathies aligned with Martin Luther's theology, could have also appealed to the reformist tendencies within Henry, especially given the conflict with the Catholic Church and the Pope's refusal to annul his first marriage.
Events took a darker turn when Anne Boleyn's supposed inability to give birth to a son led to her accusation of adultery, her subsequent execution, and Henry's marriage to Jane Seymour, who did give birth to a male heir, Edward.