Question

why we cant speak when we have hoarse throat

Answer 1

hey here is ur answer :-)
Air from lungs causes a wave on the lining of this cords ,which creates sounds. straining the folds - which can happen by attempting lower ,or greeting a cold or sinus infection - can cause irritation that results in hoarsenses.
Talking or whispering can aggravate the hoarsenses.
Hope it may helps you

Answer 2

When we sing or speak, the vocal cords vibrate and produce sound. ... The most common cause of hoarseness is acute laryngitis (inflammation of the vocal cords) caused most often by an upper respiratory tract infection (usually viral), and less commonly from overuse or misuse of the voice (such as from yelling or singing).