As a writer, you hear a lot of advice, do's and don'ts, "rules" and so forth. Some of it is good, but not all of it. One piece of advice that I keep hearing is, "make your protagonist(s) likeable or sympathetic."
Now my motto is to make a character interesting, because who doesn't love interesting stuff? I don't aim for likeable since I don't believe there's a human being alive who is perfectly likable in every way; there's always some flaw--and I mean real flaws, like negative attitudes, nasty dispositions, etc. So it seems silly to attempt that with characters. But yet, writers will try to create perfectly likeable protagonists--which ultimately backfires.
For example, Song of Scarabaeus by Sara Creasy, the main character Edie is made to be a likable protagonist: she's kidnapped by pirates (sympathy points!), she doesn't hold any real negative feelings toward her captors, and even kind of makes friends ('cause they're not sorbad after all), she tries to help out her unwilling bodyguard... You get the idea, she sounds like an awfully nice person. So what could go wrong?
Towards the end of the book, Edie and the pirate crew land on an alien world where they plan to harvest some terraform technology. However, the terraforming went terribly wrong, and now there are giant carnivorous plants. So Edie tries to play hero (mind you, she's a tech person, and has no training in the art of saving lives)--instead of, you know, getting her ass out of there. There's nothing you can do for a guy that has been swallowed up by an over-sized venus flytrap, and only his arm is sticking out. But wait--if she were abandon them, that'd be a mark against her likable nature...and we can't have that! Frankly, I would not blame her for fleeing, especially from a threat that is waaaaay over her head. It's the smart thing to do.
But it doesn't end there: Edie uses up the toxin that keeps her alive on a no-good asshat, all so he could not suffer. Nice sentiment, but the character just dug her own hole. Might as well have gotten eaten for all it's worth.
Not bashing the book, it is quite good...until you get to those last few chapters. Then all you can do is shake your head.
If you've seen the fourth installment of Indiana Jones, did you ever wonder (on top of all the many flaws) why Indie kept trusting that traitorous bastard Mac? I guess Indie never heard of the saying: Once burned, twice shy. Indie kept dragging Mac along and Mac kept screwing him over, and it made Indie look like a complete idiot. Why?! There's also a real lack of Indie doing any sort of killing--btw, I highly recommend Red Letter Media's reviews; they're hilarious (in a dark way) and the criticism is spot on.
Those are just a few examples, but you can see how trying to make a character likeable is not only constraining, but frustrating. Would it really have been so bad if Indie had shot Mac? Or threw him into a lake full of piranhas?
Whereas writing interesting characters would allow for some deviation in morality, because we're all essentially hypocrites (you can deny it, but you are one, whether you realize it or not), or a complete lack of morals. Interesting comes in many, many different flavors and you can even mix and match. Likability only has one flavor, and it's vanilla.
Think of vanilla ice cream: it's okay by itself, but it's so much better if it had toppings like nuts, chocolate syrup, sprinkles... The more varied and distinct the toppings are, the tastier the ice cream becomes.