Let us suppose an actor believes that morals are objective, and one believes they know what actions are ethically "good" and "bad".
Why should this individual bother acting in a way that is "good" as opposed to "bad", particularly if the "bad" action results in a net benefit to the actor?
After clarifying that the question should only be taken as referring to moral "shoulds" (as opposed to practical or emotional "shoulds"), which resulted in this rephrasing:
So why should something be done just "because it's right"?
The answer would have to be that there is no additional reason. A moral should is equivalent to "because it's right". In other words, the question above is like asking:
So why is 2 + 2 the answer just because 4 is the answer?
Now, whether you find the existence of moral shoulds possible or even make any sense is another question. But if you do accept them as possible, then you can't intelligibly ask what else contributes to a "should". Instead, they are, at least in non-religious systems of morals, axiomatic (in some views, though, they are products of a god's will or the equivalent and one should do something because the god wills it, and that is axiomatic).
If certain people are to be believed: you should because the "good" action is more likely to result in your passing your genes on to the next generation; or because it's more likely to result in the survival of the species.
For a full examination of this question by Christian person William Lane Craig, click here.
For a discussion affirming that "God is not required for morality" by Ronald A. Linsday, president of the Center for Inquiry, click here.
An actor should not bother about good and bad in this case. The reason behind his action may be his inability in acting. If he is a good actor his acting can influence the people in a better way even though it is a bad action.
Though the titles are not the same, I have mentioned the main thing you asked as a second part of an answer to another question. In it I have mentioned the importance from individual's point of view as well as society's point of view. I have also explained it in the minutest level at the end of the answer.
This goes in direction of the question of moral motivation. If we take "Why should we act morally?" as "What motivates us to act morally?". There are multiple views on this that usually come with certain other viewpoints in metaethics.
Why should this individual bother acting in a way that is "good" as opposed to "bad", particularly if the "bad" action results in a net benefit to the actor?
An internalist would say that this question makes no sense: if a person knows what is morally good then they will also necessarily be motivated to act. This seems to be the underlying view of one of the comments here.
An externalist would say that this question is reasonable. Their idea is that moral reasons themselves don't motivate but that we need external reasons to be motivated. For example: avoiding the feeling of guilt, seeking social standing, ...
(That's basically the main idea, but some views are mixed and things get complicated quickly. More in the SEP article.)
Now why is this a problem? Basically both views have different theories of motivation. Depending on how you combine certain claims you'll more likely end up defending views like moral non-naturalism, moral naturalism, moral non-cognitivism, ... or vice versa.
Nietzsche would say he definitely shouldn't. He should consider all effects on himself, and do what honors his own sense of power best.
If conceding to the 'good' limits him, he will come to hate it, and if it is legitimately good, that hatred is legitimately bad, so he has not really made the world a better place. In particular if the notion of good, legitimate or otherwise, violates the truth of the actor's internal perspective, he must be careful not to destroy what is unique in himself.
But real, healthy people are also not sociopaths, we love those around us, we feel for them and we are made greater by their respect for us. So your own greatest advantage might not be your own shortsighted desire. Nor is it some comforting abject capitulation to the decisions of others simply because they are more numerous and choosing them over yourself is a safe and indulgent option.
In the Gay Science he suggests that one needs to "Make of the Self a work of Art." This means that one should be willing to shape ones habits and actions in a way that harmonizes your own aesthetic and environment. A good piece of architecture fits into the landscape. But that same piece of architecture, retains and presents a vision, respects quality and durability, and honors decisions about function.
