All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
There is no doubt that parents enjoy an elevated status in Islam as prescribed by the Sharee'ah. Children are obliged to be dutiful towards their parents and treat them kindly and respectfully. Please refer to Fatwa 87019 and 84942 about the merits of dutifulness towards one’s parents. It is incumbent on children to be dutiful towards their parents to the best of their abilities.
However, children’s dutifulness towards their parents is restricted to what involves benefit for the parents without incurring any harm on the children. Children are not obliged to obey their parents in what does not bring benefit to the parents or incurs harm on the children. Shaykh Al-Islam Ibn Taymiyyah wrote, “It is incumbent on Muslims to obey their parents in what does not constitute disobedience to Allaah; this is, of course, with regards to what serves the benefit of the parents and does not constitute harm for him…” [Al-Ikhtiyaaraat]
For more benefit, please refer to Fatwa 131695.
Hence, if there is no clear benefit for your father in ordering you to cut your hair, then you are not obliged to obey him. Moreover, the father should take into consideration the fact that his daughter has grown up and has become a young woman; he should not treat her as he treats his younger daughter who may not care much about the length of her hair.
Allaah Knows best.