Fear is the opposite of faith. If you are living in fear then your not living in faith and vise versa. And yes hate is the opposite of love, if your living in fear it produces anger, bad feelings and yes possibly hate. On the other hand if you are living in love (faith) then you are living in light and are able to push aside feelings of anger, hurt, etc. however, we are all human beings therefore not perfect some of us straddle the line between faith and fear its up to us to make that choice and get back on the path if we stray into fear.