Let's consider a counter argument -
If the negation of hatred is apathy, and the negation of love is also apathy, then is it not true that love and hate are equivalent?
Consider a number of any magnitude. The opposite of a number with magnitude would, by your logic, necessarily be a number without magnitude: 0. However, 0 is not the negation of a number with magnitude - the negation of a number of magnitude is a number of the same magnitude with an opposite sign. Further, for anything that is opposite another, it is necessary that the relationship is reciprocal. The opposite of true is false, and the opposite of false is true. However, in the case of 0, while it may be possible to argue that the opposite of 1 is 0, it is impossible to argue that the opposite of 0 is 1. Reducing any number to just a number with magnitude loses a lot of the information that is contained by that number. You are losing information when you make that reduction, and thus, even if it were accurate to say that the opposite of a number with magnitude is a number without magnitude, it is not accurate to then translate that result to the original number, as you did not consider all of the pertinent information by making that reduction (for one, sign).
In the same way, It may be true to say that the opposite of an intense emotion is apathy, but it seems to me that to reduce love or hatred to just any intense emotion belittles the specificity of love and hatred. For one, love is positive, and hatred is negative, and reducing them both to "intense emotion" is to ignore pertinent information about those two things. Thus, even accepting that love and hatred are both intense emotions, and that the opposite of an intense emotion is indifference, is it possible to say that love and hate are just intense emotions. In other words, is knowing that something is an intense emotion sufficient to recover what intense emotion it is? Or is that translation not possible without more information? If it is not (and it is not), then it cannot be correct to assert that the opposite of love (or hate) is indifference solely because love (or hate) is an intense emotion, as that definition does not alone encapsulate love (or hate)