its not just about that. he hates him because his father married a human (he cheated on sesshys mom) . after sesshomaru fond out that InuYasha was born thats when the hate came. he hated father for marrying a human and having a half demon! sesshomaru could not stand humans. when 犬夜叉 obtained tetsusaiga things got worse. sesshomaru would try to kill him! but i can tell sesshomaru does not hate him 100%. when 犬夜叉 was a full demon in one ep sesshomaru came to see this power. he tried to beat inuyasha. and when 犬夜叉 was almost done sesshomaru 说 "no. im finished. there is no use to kill somone who doesnt know who they are 或者 whats going on." 或者 another ep when rin had to find the antidote for jaken who got stung 由 narakus bugs. anyways while that sesshomaru was looking for naraku who came across inuyasha. sesshomaru demanded an answer for where naraku was. 犬夜叉 had no clue but they started fighting. after a while sesshomaru had the tip of his sword to inuyashas neck. kagome 说 which way he went and he let 犬夜叉 freee. plus sesshomaru rescued a human! so sesshomaru mite not hate 犬夜叉 100%
