In true Military fashion(through out history,around the globe) why is the tyrant and his children killed?

Question

is it because his children will imitate his doctrine and carry on in his footsteps

Answer 1

Historically, often when there is a violent change of power - especially in monarchies - the children of the ousted monarch are killed to prevent anyone from having a "rightful" claim to the throne and galvanizing loyalists of the old regime.

Answer 2

Normally, a tyrant's children aren't killed, at least by Americans, unless they are adults who are following in their father's footsteps. Many countries where tyrants are ruling kill anyone, even children, who doesn't agree with them and dares to voice the fact.