The opposite of love is not hate...it is indifference.

in⋅dif⋅fer⋅ence
  /ɪnˈdɪfərəns, -ˈdɪfrəns/ Show Spelled Pronunciation [in-dif-er-uhns, -dif-ruhns] Show IPA
–noun
1. lack of interest or concern: We were shocked by their indifference toward poverty.
2. unimportance; little or no concern: Whether or not to attend the party is a matter of indifference to him.
3. the quality or condition of being indifferent.
4. mediocre quality; mediocrity.
Origin:
1400–50; late ME, var. of indifferency < L indifferentia. See indifferent, -ence, -ency

Synonyms:
1. Indifference, unconcern, listlessness, apathy, insensibility all imply lack of feeling. Indifference denotes an absence of feeling or interest; unconcern, an absence of concern or solicitude, a calm or cool indifference in the face of what might be expected to cause uneasiness or apprehension; listlessness, an absence of inclination or interest, a languid indifference to what is going on about one; apathy, a profound intellectual and emotional indifference suggestive of faculties either naturally sluggish or dulled by emotional disturbance, mental illness, or prolonged sickness; insensibility, an absence of capacity for feeling or of susceptibility to emotional influences.

Antonyms:
1. eagerness, responsiveness.