I think Hatred and Love comes together.
In both these Love and Hatred what we finally get is Suffering as I see. So is there really a connection between Love and Hatred according to Buddhist Teachings ?
Love and hatred is rooted in craving and aversion. In essence they are related as they take opposite polarity or dualism like the 2 sides of the same coin. It is so easy that things you crave for turns into aversion and vis versa. Generally is it people who were once close and deer who become foes as their shortcomings hurt the most. Also when foes to reconcile they are more friendly as they have an inclination to make up for the past. When you do not get the thing you love the most you get the most upset.
Both these are roots are associated with negative consequences, i.e., suffering follows. The methods to address this is to you have to cultivate non attachment and non hatred and finally let go of them also. Non attachment and non hatred led to positive consequences but still you are in Samsara.
Attachment <--------> Averse
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Non Attachment <----> Non Averse
I think they are connected -- at least according to Tibetan Buddhism, and perhaps according to other schools of Buddhism as well (1) -- and the connection is, as you said, misunderstanding.
Wikipedia's description of the Three Poisons says ...
Of these three, ignorance is the root poison. From ignorance, attachment and aversion arise.
... and gives several Tibetan Buddhist references for that sentence.
(1) "at least according to Tibetan Buddhism, and perhaps according to other schools":
I think that the "three poisons" (including both desire and aversion) are an important or central part of the doctrine of Tibetan Buddhism ... and, that "ignorance" (perhaps what you called "misunderstanding") is seen as the "root" poison from which condition the other two.
That may also be true of other forms of Buddhism too, but I'm not sure. The "three poisons" are in Theravada suttas (sometimes also known as "three fires") but maybe they emphasize craving more than aversion. For example in this Theravada respresentation of the Wheel of Life, the "three poisons" aren't at the centre and in fact "aversion" isn't shown at all. Instead there are several conditions or causes: including ignorance but also desire, attachment, fabrication.
Actually "aversion" seems to be in Theravada as one of the defilements (kilesa) rather than as one of the causes (nidāna).
Returning to the Pali suttas, something like the Vipallasa Sutta: Distortions of the Mind (AN 4.49) warns what the misunderstanding (or ignorance) might be about: that fundamentally it might happen at three levels (perception, thought, and view), and on three four characteristics (impermanence, dukkha, and anatta, and subha).
