How could his father agree to his renunciation?
他父亲怎么会让他出家呢？

Having found out what his son had in mind, King Suddhodana tried many ways to detain him, especially by surrounding him with worldly pleasures. When Siddhattha was only 16 years old, King Suddhodana arranged for him to marry Princess Yasodharā from a neighboring state. Yasodharā bore him a son named Rāhula. But all this was in vain. He finally slipped out of the capital city in the still of a night. He entered a forest, took off his princely clothes and, having shaven his head and beard, became a wandering mendicant. Regarding his age at the time of renunciation, there are two different accounts—one says nineteen, and the other twenty-nine.
净饭王发觉了他儿子的心思后，曾经想过各种办法防止他，特别是企图从生活的享受上羁縻他。悉达多王子十六岁时，净饭王便为他娶了邻国的王女耶输陀罗（Yasodharā）为妃，生了一个儿子叫罗怙罗（Rāhula）。但是这一切都没有能够阻止他，终于在一天夜深人静的时候，他偷偷地出了国城，进入一个森林中，换去王子的衣服，剃去须发，成为一个修道者。关于他出家时的年龄，有两种不同记载，一说是十九岁，一说是二十九岁。