Hi, I'd like to help you with your question.
It depends very much on the situation and the type of person you are. For example, if you tend to be a dependent person who looks to others for help in every situation, then being self sufficient is a good thing. But if you are always doing things on your own no matter the consequences, then self sufficiency is not good for you.
For most people, finding a balance between being self sufficient and being dependent is difficult. Each person decides for themselves the limits of self sufficiency. Some people feel guilty asking for help. They were taught growing up that you rely on yourself. Some had their parents, particularly fathers, equate self sufficiency with manliness, pride or worth as a person. And some people were raised to expect others to do for them. Or even that they cannot do for themselves because their is something wrong with them. Still others were taught how to rely on others by how their parents treated them and others.
Self sufficiency is also gender related. For females in particular, self sufficiency is a two edged sword. Being self sufficient means you are man like. But being too reliant on others makes you lady like and appealing to men but you are seen as having low intelligence. For men, it is opposite. Being self sufficient is almost expected to the point that there are jokes about it in our society (for example, men don't ask for directions, as a rule). Self sufficient men are celebrated in our society.
So you can see that self sufficiency is a subjective and culture based characteristic. Factors such as how you are raised, relationships, personal beliefs and gender all play a part in deciding how self sufficient someone is.
I hope this helps,