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 inuyasha obtained tetsusaiga things got worse. sesshomaru would try to kill him! but i can tell sesshomaru does not hate him 100%. when inuyasha was a full demon in one ep sesshomaru came to see this power. he tried to beat inuyasha. and when inuyasha was almost done sesshomaru said "no. im finished. there is no use to kill somone who doesnt know who they are or whats going on." or another ep when rin had to find the antidote for jaken who got stung por narakus bugs. anyways while that sesshomaru was looking for naraku who came across inuyasha. sesshomaru demanded an answer for where naraku was. inuyasha had no clue but they started fighting. after a while sesshomaru had the tip of his sword to inuyashas neck. kagome said which way he went and he let inuyasha freee. plus sesshomaru rescued a human! so sesshomaru mite not hate inuyasha 100%
