• 害虫がいちゅう — harmful insect
• 公害こうがい — pollution
• 災害さいがい — disaster
• 障害しょうがい — obstacle / disorder
• 被害ひがい — damage / suffering
• 加害者かがいしゃ — perpetrator

The top 宀 suggests a roof or house, while the lower part 豈 (phonetic + meaning hint) relates to misfortune. 害 has long conveyed the sense of injury or harm — both physical and psychological. In modern usage, it's often part of legal or social terms.

台風たいふうで大おおきな被害ひがいが出でた。
There was major damage from the typhoon.

害虫がいちゅうを駆除くじょする。
We eliminate harmful insects.

公害こうがいは 社会しゃかいの問題もんだいです。
Pollution is a societal issue.