In our usual day to day tasks we think of ourselves as good and then we try to act in such ways as to reinforce this belief. We try to justify our behaviours with the best possible reasons even if our actions were bad.
However, if I suppose that I am intrinsically bad and I don't try to justify my actions, then what? Does that mean that I am free of any morality? Then, is there any other reason except social obligation to prevent me from doing wrong?
Depends on what you mean by "free of any morality".
It sounds like you're asking:
If I don't feel a sense of personal responsibility to act "good", is there any reason why I shouldn't act "bad" other than the practical consequences I will experience in society?
This is a deep question that's as old as philosophy itself, and modern philosophers still debate many of its related ideas.
One of the most famous attempts at answering it is the story of the Ring of Gyges from Plato's Republic. According to Wikipedia, the answer, argued by Socrates, is in essence (paraphrasing):
If your decision to act "good" or "bad" is based purely on calculation of personal profit (taking into account social obligation), then you cannot have a just or happy existence since your actions are motivated purely by your appetites and desires, which you did not choose-- therefore you are not a rational agent but merely a slave to your own desires. Thus freedom and the good life comes from having personal moral agency, not from experiential enjoyment.
Socrates is saying that there is more to life than enjoying the fruits of your actions, and that what makes life truly good is having the personal power to decide how you want to act rationally, independent of your desires, and whether society obliges you to act a certain way. And Socrates is introducing a source of moral value derived from the virtues of human agency that he believes is more important than pursuing pain and avoiding pleasure.
Clearly Socrates believed what he said, since he chose to die for his ideals (famously, he was forced to drink hemlock) rather than submit to societal obligation. But you may not find his argument convincing, and not all philosophers do.
More generally, the modern debate is about "moral realism", or, in simple terms, whether ethical statements are objectively true of false, independent of the perspective of any individual. This is a big topic and an active research area today.
Most moral theorists and theories see morality as an inescapable obligation, and not something you can declare yourself free of by fiat. Let's say, however, that you reject all of those. Is there any downside?
A) Plato (as Max Wallace's answer indicates), as well as many other moral theorists, believes that acting immorally is personally harmful --it makes you a prisoner of your own worst impulses. If you believe in the soul, it might also be considered soul-damaging.
B) Some people believe there is practical value to "values." There is some evidence that immoral behavior can bring short-term gains and advantages, particularly during "good times," but that good morals help individuals and communities thrive over the long term, and/or under harsh conditions.
The Apostle Paul, a prominent first-century Christian, wrote:
We know that the law is [true, literally "spiritual"]; but I am unspiritual, sold as a slave to [immorality, literally "sin"]. I do not understand what I do. For what I want to do I do not do, but what I hate I do. And if I do what I do not want to do, I agree that the law is good.
Letter to the Romans, Chapter 7, lines 14-16 (NIV, emphasis and paraphrase mine)
I don't think it works to claim that being immoral resolves moral obligation, by the definition of the word "immoral"; here is an author who claims to be immoral himself, and who says that this claim reinforces moral obligation.
People might think this is connected to fear of rejection. This is not about rejection. See the folowing reasoning. If you smell bad, you will produce rejection. But all of these are about aesthetics. If rejection is the case, should we speak about aesthetical responsibility? Sounds weird, right?
Also, there are many local rules. What is wrong in one society can be considered good in another. And then we cannot drag in survival here.
Regarding responsibility. What is that? If you broke your own glass at home, you probably would feel uncomfortable. Because you need to buy a new glass and clean the place from its fragments. If you have empathy and you broke your friend's glass, you probably would feel uncomfortable as well. It depends on her economic conditions as well. Up to the degree that if hers are worse than yours, you can feel even more uncomfortable than if you broke your own glass. And you probably would like to excuse at least.
But the person you describe is bad. Lacks any empathy. Does not feel uncomfortable when breaks someone's glass except his own. Does it mean he will not excuse? Not really. He might not want to spoil relationships with his friend and will excuse. For his own sake, of course.
But what is responsibility then? Just a feeling that you did something wrong or right? But what is moral responsibility then? When you made a silly mistake and failed an exam are you morally responsible for that? When you committed a crime and left evidence for that are you morally responsible for leaving them? Note, you are not legally responsible for leaving them, law does not punish you for leaving evidence but for commiting a crime.
So, if you think these are moral responsibilities, which is suggested by MauroALLEGRANZA's comments (one could blame herself for commiting a mistake or leaving evidence), a human lacking them is inconceivable. If you think they are not, there are no moral responsibilities.
There was a comment by Conifold that people do not use reasoning when commiting actions. Well, they use intuition in most cases. Indeed, sometimes people can not give you a reason better than "I wanted to". Sometimes they can't be explained, like "Why did you want to eat chocolate?" and then it is not intuition. In many cases, though, they can. Intuition works with reasons. People just can't formulate them as soon as they are asked. Sometimes intuition might be wrong: if you put a yoghurt packaging to a sink and throw a spoon into a garbage can, you, probably, won't argue you had a reason for that.
