There are various reasons why the island "banished" Ben. There are some such as his attempt to prevent Locke's assumption of power, failing to protect the island, and lying to his people. However there is one reason in particular that sealed Ben's fate. One reason is responsible for "Jacob being happy" as a result of Ben's departure.
Many question how "The Other Woman" was relevant to the season 4 story line. With some in depth analysis using some religious matters as a paragon, the secret behind "The Other Woman" should seem far less ambiguous.
The Catholic Church forbids priests from participating in the sacriment of Holy Matrimony. The reason for this is that if a priest were to marry, God would no longer be his sole love in life. Transfer this logic to the realm of Lost. In "The Other Woman," Ben put physical attraction to Juliet ahead of the well-being of the island and its inhabitants. Jacob and/or the island did not take kindly to this. Ben's new committment to Juliet greatly angered the island, serving as the primary reason for Ben's banishment, and makes "The Other Woman" a relevant contribution to Season 4.
Theory by Matt4
Many question how "The Other Woman" was relevant to the season 4 story line. With some in depth analysis using some religious matters as a paragon, the secret behind "The Other Woman" should seem far less ambiguous.
The Catholic Church forbids priests from participating in the sacriment of Holy Matrimony. The reason for this is that if a priest were to marry, God would no longer be his sole love in life. Transfer this logic to the realm of Lost. In "The Other Woman," Ben put physical attraction to Juliet ahead of the well-being of the island and its inhabitants. Jacob and/or the island did not take kindly to this. Ben's new committment to Juliet greatly angered the island, serving as the primary reason for Ben's banishment, and makes "The Other Woman" a relevant contribution to Season 4.
Theory by Matt4