In answering the question why we should care about an author’s intention, C. S. Lewis gives two answers in his book An Experiment in Criticism.

"Why," they ask, "should I turn from a real present experience—what the poem means to me, what happens to me when I read it—to inquire about the poet’s intentions or reconstructions, always uncertain of what it may have meant to his contemporaries?"

There seem to be two answers. One, is that the poem in my head which I make from my mistranslations of Chaucer or misunderstandings of Donne, may not be so good as the work Chaucer or Donne actually made.

Secondly, why not have both? After enjoying what I made of it, why not go back to the text this time looking up the hard words, puzzling out the allusions and discovering that some metrical delights in my first experience where due to my fortunate mispronunciations, and see whether I can enjoy the poet’s poem, not necessarily instead of, but in addition to my own. (100-01, paragraphs added)

I would add two more.

1. Courtesy
   
   Treat authors with respect and seek what they were trying to communicate. I call it the hermeneutical Golden Rule: Do unto authors as you would have them do unto you. Most of us are offended if someone spreads the rumor that we said hurtful x, when in fact we said helpful y.

2. Authority
   
   If we are reading the Bible, it’s authority lies in the author’s intention (ultimately God’s) not our perceptions. We honor the authority of scripture by doing the hard work of thinking authors' thoughts after them.