I agree with this. We are commanded to love God and to love others as ourselves. Where there is love, there can not be hatred. Just as where there is light there can not be darkness.
Then why does it exist? God is love and light. By existing, He creates their contrast. Anyway, your Bible disagrees with you:
Ecc 3:1 For everything there is a season, and a time for every matter under heaven:
Ecc 3:2 a time to be born, and a time to die; a time to plant, and a time to pluck up what is planted;
Ecc 3:3 a time to kill, and a time to heal; a time to break down, and a time to build up;
Ecc 3:4 a time to weep, and a time to laugh; a time to mourn, and a time to dance;
Ecc 3:5 a time to throw away stones, and a time to gather stones together; a time to embrace, and a time to refrain from embracing;
Ecc 3:6 a time to seek, and a time to lose; a time to keep, and a time to throw away;
Ecc 3:7 a time to tear, and a time to sew; a time to keep silence, and a time to speak;
Ecc 3:8 a time to love, and
a time to hate; a time for war, and a time for peace.