The first thing we need is a rigorous narrowing of the question. Our question is not "Can normal human beings choose the emotions they will feel?" -- it's just "Can normal human beings choose the emotions they will feel in response to verbal abuse?" It has been proposed, somewhat forcefully, that they can, and that doing so is a skill that can be learned. The second thing needed is a reminder that -- as with many other characteristics -- normal human beings vary in their reaction to verbal abuse, not in an either/or fashion but along a continuum. There will be a handful of people who are essentially indifferent to it at one extreme, and a handful who are literally incapcitated by it at the other. The vast majority of individuals will fall in between those two extremes, and it's that majority that we've been focusing on.
In order to deliberately choose the emotion you will feel, you have to be able to consider the various choices rationally and decide among them, even if you do that at lightning speed. Your human brain isn't set up ideally for that process. Instead, one part of your brain -- the amygdala -- is on permanent red alert, always scanning for possible danger, and it has the ability to cause you to act before the threatening information can reach the reasoning part of your brain. (Daniel Goleman calls this phenomenon an emotional "hijacking," and the term strikes me as apt.)
When a two-year-old child charges at you with clenched fists, screaming with rage, your amygdala doesn't kick in; the idea that you're in danger would never cross your mind in that circumstance. You remain detached and rational; you're able to investigate the situation and find out why the toddler is in such a state; you're able to come to a decision about how best to deal with the problem.
If you perceive verbal abuse as an attempt to harm you, your amygdala is likely to take over and determine your emotional reaction for you; if this happens, there's not one thing you can do about it. It's part of your human heritage. This was very handy in the days when you might encounter a sabertooth tiger the instant you stepped outside the cave; it's not as handy in today's world. But it's not under your voluntary control, it's the way you -- as a normal human being -- are wired. And so most of us have had the experience of suddenly realizing that we're in the middle of a screaming match over something we don't really care about at all, wondering "How on earth did this happen?"
Most verbal attacks aren't meant to hurt their targets. The attackers know the words will hurt, but causing pain isn't their goal. Their goal is to get human attention -- something all human beings need badly -- and they've learned from experience that verbal attacks are a reliable way to accomplish that goal. If they knew how to get attention in some more positive fashion they'd do it that way, but they're like little kids who'd rather be spanked than ignored: Since they have no idea how that's done, they'll settle for what they do know how to do.
The key to being able to "choose" your emotion in verbal confrontations is knowing how to tell the difference between the attention-seeking verbal attack and the far more rare attack that is a genuine threat and that has causing you harm as its primary goal.
This is not a simple question, and it doesn't have a simple answer.