Especially at that time, following Jesus was a dangerous thing to do. Doing so meant that one would likely alienate one's family, perhaps even put them in danger. A person must "hate" their family to put them through that. Worse, many of His followers faced torture and death. A person must "hate" their lives to be willing to follow Him in spite of such threats.
Today, the threats aren't quite as strong, but the difficulties and alienation can still exist. It is still quite possible to be mocked, derided, and shunned for holding to the teachings of Jesus and His Church. However, I am fully willing to face such opposition as I believe that Jesus not only holds the keys to everlasting salvation, but to making the world a better place in the here and now.