If this person is an individualist, he or she is likely to overlook the social connections involved and take the full credit for his or her success. Not only might this person be ungrateful, he or she is likely to be unsympathetic toward people who don't have the right connections themselves. Individualists tend to look at those who are unsuccessful as being at fault for their lack of success. This is only one of the problems with individualism. Another is that it encourages people to be competitive rather than cooperative.
Individualists tend to be out for themselves, often at the expense of others.
Say it isn't just that you happened to be in the right place at the right time, but that you have the special qualities of grit and determination that got you where you are today. Still, this doesn't mean that it's always better to emphasize the good of society over the good of the individual. Western philosophy from Plato to the 17th century focuses on the individual's relationship to ideal truths. Western science has largely focused on the individual's relationship to physical laws of nature. Western capitalism has focused on the individual as an economic unit.