Why is the quality of loyalty being HIDDEN throughout "King Lear"?I am confused by the question that the teacher is trying to ask.
I disagree with your teacher that Cordelia's loyalty is not evident at the beginning of the play (that is, it is evident to everyone except King Lear himself!). Her no-nonsense attitude towards her father and downplay in her statements ring truer to the ear than the gross flattery and currying for favour displayed by her sisters. The reader picks up rather quickly that an ultimate storm is brewing in family relationships, and the outcome is not really as much of a surprise as all that. Lear is outraged that his youngest daughter does not acknowledge his self-exalted omnipotence, but the fact that she tries to curb is meglomaniac tendencies is proof enough that she really loves him. The fact that Cordelia takes care of her father once his two other daughters have pillaged him and turned him out is consistant with her character profile.
However, I admit that this may be a modern interpretation as our mind-frame is quite different today. At the time that 'King Lear' was written, family roles were different with a definite paternal dominance into play. In this respect, Shakespeare is ahead of his times when he develops such characters as Cordelia in 'King Lear' and Desdemona in 'Othello,' both challenging paternal authority when arbitrary, demeasured and even vindictive by nature.