When asked why, Xiaomi had the same reason to give as Apple. According to the quote given to Android Central, not having the headphone jack allowed Xiaomi to make space for other components, such as a bigger battery. Indeed, the Mi 6 has a larger 3350mAh battery over the 3000mAh one on the Mi 5 despite being roughly the same size.
With the headphone jack gone, the Mi 6 now relies on the USB-C connector to output audio (apart from Bluetooth). Xiaomi says that USB-C audio is now becoming more common and will continue to provide excellent audio quality.