Why do Both Tanjiro and his Dad have the same scars?
Tanjiro told that, although the scar looked like a demon hunter mark, it hadn't been one until he mastered the mark, as wiki summarizes it:


  He also has a scar on the top left of his forehead, which he received
  when he protected his younger brother from a falling brazier. The scar
  originally looked somewhat like a graze until his fight with the Hand
  Demon during the Final Selection, after which it develops into his
  Demon Slayer Mark.