It is certainly more ideal for a person to have high self esteem and also the security to admit fallibility, but the two are not mutually exclusive. Self esteem is exactly what it sounds like - how highly a person values themselves regardless if their belief is justified in the right context, morally or not (What Vaniver says goes into this better). Self esteem that is incongruent with reality or the context is the issue here, which is why programs that simply seek to boost self esteem without also teaching proper skills that can justify high self esteem can create narcissistic individuals. Your comment below identifies this by indicating instability.
This also means that being unable to react well to criticism does not indicate low self esteem - you cannot assume a connection, let alone directionality based on your purported view of self esteem.
I think the purpose of testing an understanding of literature is testing critical thinking and argument skills (when it's not guessing the password, of course). With that said, I think philosophy classes can facilitate a more rigorous learning environment for that purpose.