Why does throat cancer cause horseness?

Due to encroachment : Hoarseness is caused by probelms affecting the larynx(voice box). So any cancer in the throat and neck areas which either invades the vocal cords or interferes with the nerve(recurrent laryngeal nerve) that controls the vocal cords, can cause hoarseness.

Irritates Vocal Cord: The cancer or the treatment either can irritate the vocal chords. Some patients have permanent damage but most will resolve with time - though it can take months or years. A speech therapist can help once tretment is complete.