Emotion drives everything we do, and I do mean everything. Logic is important, but logic itself has no power to bring us to a new place and create change. Just look at all the people who are dying of heart disease that know they need to change their diets in order to live, but refuse to do so. Logic says, "Eat right or die", and they respond with, "I care less about dying than I do about eating whatever I want, whenever I want."
In other words, logic only moves us when we care enough to move on it.
I saw a sci-fi movie once (not giving the name to avoid spoilers - those who have seen it will know what I'm talking about) where the characters land on a planet that has dead people just sitting in cars, at desks, lying on the street, etc. No violence was committed anywhere. They discover that the government of the solar system was experimenting with a drug to make the population more docile, but it succeeded so well, they were stripped of all emotion. They literally starved to death, knew they were starving to death, but simply did not care enough to do anything about it.
If we were stripped of emotion, we would do the same. Unfortunately (or fortunately, rather), negative emotion brings a lot of pain. Who likes to feel betrayed or depressed or angry or sadness or grief? All of these emotions are unpleasant, but what's more, when they hit, our brain shuts off and we lose some of our higher thinking functions. Fight or flight literally pulls blood from the brain and into the heart, and so we make stupid mistakes. The things we say when we are angry are almost always not things we would say when we were calm. Arguments and debates are often lost by the person who lets their emotion get the better of them.
Our reaction to negative emotions are often to clamp down on them, hard. We don't want to feel those things, so we do our level best to bury them deep enough that they rarely push up into conscious thought. However, this approach also removes our ability to feel joy and happiness. Emotion is emotion, and if I reject the hard and painful emotions, I also reject the profound and enjoyable ones. Addictions often emerge as a substitute for genuine positive emotion - pleasure certainly feels good, but it is hollow, lacking the ability to make us a better person.
Not that we should swallow our negative emotions whole because that would be akin to burning my hand on the stove and not removing it. I feel pain because I am damaging myself in some way, and negative emotions provide the same warning - we are doing/saying/thinking/believing something that is damaging to us, and it needs to be solved. But when I accept the role that negative emotion brings to the table and use it as impetus to solve my problems, I also open the door for true happiness, love, gratitude, and the whole host of positive emotions to reign in my life as well.
If I cut off negative emotion because I don't like suffering, I compound my suffering, for I also cut off true joy.
In fact, when I accept the proper role of negative emotions in my life, as symptoms of a deeper problem in me that needs to be fixed, then I am driven towards deeper and richer happiness in my life.
If you want to be happy, accept the role of emotion in your life, painful and joyful both.