Why are we not allowed to see the Lord’s face and live?

The Bible does not give a reason why.  Therefore, any answer given is simply supposition and theory.  Personally, I think the reason God does not allow us while in human form to see his face and live is so that our faith will be strengthened.  I’m reminded of what Jesus said to Thomas once Thomas had actually seen and touched him after his resurrection:  “Have you believed because you have seen me?  Blessed are those who have not seen and yet have believed” (John 20:29).

(Since giving this answer, I had an opportunity to discuss the question with the person who had asked it.  They proposed the theory that we are not allowed to see the Lord’s face and live because we are not worthy.  That may well be true.  Again, we cannot know for sure without biblical revelation.)