A classic saying that is surprisingly accurate in more than one way. The fine line between love and hate could be very well a main reason we have war to begin with. That's not to say that without love there'd also be no war, but I'd wager it would be significantly reduced. Significant and substantial are two different things though, while it would be noticeable it would be far from gone, particularly now that factor is shrinking in this day and age when war is primarily fought over resources.
To illustrate a small point I'll offer an example that perhaps you can relate to. Most people in my experience are less aggravated by other people of completely different beliefs on a given subject than those that have similar but not the same beliefs. It can be more aggravating that someone who seems to know a subject is slightly wrong or comes to a different conclusion than someone that denies it all together. For a gaming example let's say you have 3 people in a group chat discussing first person shooters. You and your friend believe Modern Warfare is the best while the other person is merely a guest and proclaims Battlefield is the best. This is usually a civil conversation though it can get heated just as easily as any other. Yet consistently if you and your friend do not share the same opinion on what the best gun is or even what the best gun of a given type is the conversation can turn into an all out shouting match. As you each hold your firm belief in something so similar it becomes inconceivable for anyone that otherwise agrees with you on the subject to disagree with you on such an important factor. This holds true in other subjects as well not just gaming.
While it's not universal there is a clear dominance on the subject. You can easily hate someone because you love them, you'd rather teach them a lesson than let them be. While you'd simply let a stranger go on to make a mistake when they disagree with you yet you'd get in a fist fight with a friend to prevent them from making that same mistake. Yet another classic which we may all know is how two people can love each other and yet one of them may do something so simple yet so profound it can send the other into a blood rage forever ending their relationship.
For an introspective look think about something or someone you hate and think about specifically why you hate it/them. Question your answer several times over and see if perhaps you discover something new you didn't know or understand before.