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I'm not saying I sweep things under the rug. I think this is as much of a misconception regarding Fi. I simply prefer to discuss things in a calm manner. Seeing someone express themselves to me in an overly emotional manner will immediately cause me to shut down. This doesn't, however, mean that I don't want to talk about whatever might be going on. I have a hard time believing that someone who is not able to keep their cool and maintain "civilized" conversation and will instead resort to yelling and name-calling, is capable of maintaining a healthy relationship. Maybe this is just coming from an Fi point of view. Different things work for different people. I just don't personally see myself able to endure a situation like this, especially if it's a frequent occurrence. But again, I do believe in open communication and talking about things. It is "how" this communication happens that differs, I think.
What exactly about emotional outbursts make you uncomfortable? The way they affect your emotional state? Or because you feel the other person is in an unstable state? What if you knew that the person was using their emotion as a vehicle of self-expression rather than deliberately trying to affect you? That they were completely in control. Would that bother you still?
"Language is the Rubicon that divides man from beast."