Does permanent hair dye damage hair?

well im a 14 year old girl who absolutely hates her natural hair color. i would like to go to the salon and get my hair dyed a darker shade of brown than i already have, but my dad wont let me, he thinks that it damages all of your hair, even the stuff that grows after its dyed. my mom has no problem taking me to the salon because she has dyed my hair sense i was in 3rd grade, and when i was going into middle school she messed up on hair dye that turned my whole head platinum blonde. so she says that if i want my hair dyed again then i have to go to a salon to do it so if they mess it up then they have to give me my money back or they will have to fix it...ive wanted to dye my hair dark brown with burgundy streaks sense the middle of 8th grade, and i really would like to do it soon