The relationship between equality and personal success in life
In my opinion, an egalitarian society is one in which everyone should have the same rights and the same opportunities. I completely agree that people can achieve more in this kind of society.
Education is an important factor with regard to personal success in life. I believe all children should have access to free schooling, and higher education should be either free or affordable for all those who chose to pursue a university degree. If a society without free schooling or affordable higher education, only children and young adults from wealthier families have access to the best learning opportunities, and they would therefore be better prepared for the job market. This kind of inequality would ensure the success of some but harm the prospects of others.
I would argue that equal rights and opportunities are in conflict with people's freedom to succeed or fail. In other words, equality does not mean people lose their motivation to succeed, or that they are not allowed to fail. On the contrary, I believe people would feel more motivated to work hard and reach their potential if they thought that they lived in a fair society. Those who did not make the same effort would know that they had wasted their opportunity. Ineuqality, on the other hand, would be more likely to demotivate people, because they would know that the odds of success were stacked in favour of those from privileged backgrounds.
In conclusion, it seems to me that there is a positive relationship between equality and personal success.