One of Shakespeare's more central points in the play is to show the harmfulness of intense, passionate, violent, uncontrolled emotions as opposed to calm, rational, reason. That's one reason why both love and hatred are in the play. Shakespeare is not showing them to be emotions that are polar opposites. Instead, he is showing that violent, uncontrolled love is just as harmful, even deadly, as violent, uncontrolled hatred and that there really are no clear distinctions between the emotions. Hence, hatred is an underlying theme of the more central theme concerning uncontrolled emotions vs. rational thought.
One place in which we can clearly see that Shakespeare wants to show there is very little distinction between violent love and violent hate and how both are harmful emotions is in Romeo's early speeches in the very opening scene. When Romeo sees the damage left over from the opening battle scene, his first response after asking what has happened is to point out, "Here's much to do with hate, but more with love. / Why then, O brawling love! O loving hate! ..." (I.i.173-74). While in this speech he is moaning over Rosaline's rejection, these lines also characterize the entire essence of the play. Romeo is pointing out that the Capulets' and Montagues' brawl has just as much to do with hatred as it does with love--that there really isn't a clear distinction between hatred and love, especially because both are violent, irrational emotions. He is pointing out that the reason why the two families are feuding is because they hate each other, but more importantly, they hate each other due to what we could call love. They hate each other because they love themselves, their ideals, and their principles, which they think are so much more important than the other family's ideals and principles that they must fight each other. Hence, Romeo is extremely correct to point out that their feud has as much to do with love as hatred and even that hatred can be caused by a certain violent, irrational, uncontrolled love. Therefore we see Shakespeare's central point is to assert that there really are no clear distinctions between love and hatred and that both emotions when allowed to be violent, irrational, and uncontrolled can lead to just as much damage in contrast to the use of the rational mind.