Miley Cyrus sings through her nose because that is how she naturally produces sound. Some people naturally produce sound with a nasal quality to their voice, and this is known as nasality.
Nasality is a result of sound being produced in the nasal cavity and resonating through the nasal passages, which can give the voice a distinctive quality. It is not uncommon for singers to use their nasal cavity to produce sound and add character to their voice.
Some people are more prone to singing with a nasal quality due to the shape and size of their nasal passages. There is no one specific reason why Miley Cyrus sings through her nose, but it is likely a natural part of her vocal production.