I am inspired by many consequentialists and utilitarians. For example, I think the staff at GiveWell do really interesting work. If we want to fulfill our obligations to the worst off, we should very critically examine the aid organizations that purport to use our money well in providing services. GiveWell does an excellent job of promoting well-researched methods of providing aid done by programs who can effectively use large inflows of capital. This is good and important work that people of a utilitarian or consequential mindset (like those who started GiveWell and many of its supporters) seem very skilled at doing.
I find it to be a failure of many non-consequentialist philosophers that, though their theories would demand strong levels of support for meaningful philanthropic work, they often fail to sufficiently support this kind of action. Many are reluctant to give specific prescriptions of how individuals can better meet their moral obligations, which to me comes close to rendering moral philosophy pointless. (Gary Francione is a particularly important exception to this trend.)
Nonetheless, I find non-consequentialist moral theories compelling, and think there are many things wrong with consequentialist or untilitarian moral theories. Despite my (admittedly anecdotal) observations about the actions of adherents to the different theories, I think there are very good reasons to reject consequentialist moral theories, which I've discussed in brief previously (also here and here.)
But if the implications of consequentialism are implausible, as I argue, why do people believe in it? Well, as I've been discussing, there are often good reasons to accept conclusions that at first seem implausible. When confronted with a surprising consequence of a theory, there are a few ways of responding.
First, you might be facing a dilemma. There might be an implication of a particular theory that is implausible, but denying that theory as a whole has even less implausible implications. We should in these cases accept the most plausible alternative.
Another way to respond without appeal to prima facie plausibility judgments is to show that the reason a given implication appears implausible is because we are have an unjustified bias against what is implied. This is how my argument against speciesism works. Obviously, to many people it is implausible that animals should be granted fundamental rights. However, if speciesism is a bias just as sexism and racism are, it's no wonder that animal rights are counter-intuitive. We should expect overcoming such a pervasive bias to lead us to conclusions that contradict deeply-held beliefs we held previously.
So many consequentialists see the supposedly "implausible" implications of their view as the result of our unjustified bias towards consequentialist morality. As they might rightly point out, our minds are infused with a variety of biases and predispositions towards fallacious inferences, it's hardly surprising we would intuit wrongly about some moral issues.
Just as I see the fall of speciesist prejudice as continuing a history of the (one can hope) fall of sexism and racism, a consequentialist might similarly see non-consequentialist judgments going the way of the belief that the earth is flat, or that the phase of the moon controls behavior. A bias against consequentialist reasoning is not going to function like racial bias, but something more akin to psychological effects such as confirmation bias. Some ways in which we are predisposed to think are fallacious. There might be any number of reasons why we are predisposed to think them, but once we have a good theory to sort out the fact from the fallacy, we might as well jettison whatever we got wrong.
The problem with this line of argument in favor of consequentialism is that there is not good enough reason to believe that, for example, the principle of utility is the fundamental principle of morality. It may look alright, at first glance, that we should maximize happiness for the greatest number, but it's obvious enough that other things matter as well. For example, I think certain forms are inequality are inherently bad, even if many people are made very happy by them. It's conceivable to me that the greatest happiness for the greatest number could involve some insidious inequality that would make me strongly loathe such an outcome. Perhaps this is just some irrational bias of mine, but who says? Why isn't feverish devotion to the utility principle the unjustified bias?
So you might say the utility principle isn't inherently more probable than a theory that has a greater variety of values in it, such as equality. But why shouldn't we want to find some maximally optimum balance of equality and happiness (and perhaps some other values)? Well, certain forms of this type of consequentialist theory can be compelling, but my post against the maximization of friendship is a pretty good rejoinder to these. Some important values do not appear amenable to maximizing treatment. And again, why should we think of a maximizing moral theory as inherently more appealing than a theory that can make sense of our common views on friendship?
One reason that I think holds some sway over many consequentialists is the relative simplicity of their theories. If consequences are what matter, it's very clear how to choose the right thing. The tricky part is adding up the different probabilities of different outcomes, assigning values to different features of the situation, and weighing these all against each other. But as I noted at the beginning of the post, many utilitarians are very good at doing all this, and do an admirable (!) amount of good in so doing. It's a lot messier if there are attitudes of respect to consider, and deontic contraints, distinctions between killing and letting die, etc. There are likely to be some meta-ethical concerns about the truth value of non-consequentialist theories, which would have to apply to more than just features of the natural world. (I'll pursue this topic later.) Many people appreciate the beauty of a simplified theory.
If we have good reason for doubting that there is such a simplified theory, then another example from the history of thought comes to mind. When Newton discovered the laws of motion, they were truly revolutionary and brilliant, and they had fantastic predictive powers. One can imagine getting very excited about such a genuinely elegant theory that held together so well and explained so much. It took Einstein and a lot more work to discover that around the edges, the theory didn't explain everything, and on certain scales was not as accurate as had been thought.
Sometimes theories have to be intricate and complex to explain all the features of the world that we encounter. Simplicity can be a virtue of theories, but it can also lead to obfuscation. Perhaps it would be easier to live in a simpler landscape, but I certainly enjoy the process of discovery.