I don't answer the phone when I don't feel good, but some people feel like the have to (answer it).
If the phone rings and I don't feel good, I don't pick up, but some people feel obligated to.
最後の「answer it」は抜いても大丈夫です。
feel obligated to = ～する義務があるように感じる
電話に出る = answer (the phone), pick up (the receiver)
今は携帯・スマホの時代ですが、まだ「pick up」という人がいると思います。
アメリカ合衆国 
