The hearth and the Salamander can also mean happiness and if Montag chose to be happy or not. The two things in his life his home and his work. Did it really make him happy. He chose happiness over this home and his work by reading the books.
"Why does it hurt so much?" "Because it matters. Because you love with a tenacious love. Hurt is just the predecessor of love and anger is just the predecessor of hurt. You have a deep anger because you have a deep love.