Tybalt is responsible for Romeo and Juliet's deaths because his insistence on fighting Romeo is what got Romeo banished and led to his death. Tybalt was so caught up in his family feud that he did not think about the consequences.
The paragraph first says what is being compared and contrasted, then it says what they have in common by using the word "both." The phrase "on the other hand" shows that they're being contrasted.