Why do you think Sor Juana Ines de la Cruz is opposed marriage and public life?
Having only just recently read Sor Juana's responses in "Respuesta a Sor Filotea" and researched her life for the first time, I get the sense that she is passionate about learning, even from a very young age. She cannot be dissuaded from reading, and some sources report that she secretly read books from her grandfather's library, and even considered herself self-taught because an education was not available for young ladies.
Achieving so much at such a young age, I would expect that Sor Juana was a practical and wise young woman. With such a passion for learning, and still so much left to study when a girl her age would have been considering marriage, two things may have influenced her.
First, a husband might not have condoned her study; if he did, having the responsibilities of wife, mother and home would have made it very difficult for her to pursue her education. And in convent life, especially the one where Sor Juana finally ended up, the lifestyle was extremely conducive to tranquility, and would have allowed all the opportunity Sor Juana could have hoped for in order to continue with her learning.
The second reason may come from the writings of Paul. In the first book of Corinthians 7:27, Paul states that to truly be committed to God's work, it is better not to marry. It is possible that Sor Juana had read this and agreed with it.
However, if I had to choose one reason why I felt Sor Juana chose not to marry it would be to provide her greater freedom to study.
In terms of choosing to lead a more secluded and less public life, as with many people who are particularly bright, keeping up a social life is difficult in that it takes one away from his/her studies, research, etc., and it is sometimes hard to relate to people who are not as passionate as that extremely intelligent man or woman.