Because he was good at English, this earned him the enmity of some people around him.
ご質問ありがとうございます。
"Because he was good at English,"＝「彼は英語が良く出来たため。」
"This earned him the enmity of some people around him."＝「彼の周りの人間の一部から反感を買った。」
☆ 日常会話ではあまり"enmity"という単語を聞いたことがありませんが、どちらかというと文章語、又はフォーマルな場面で使われます。
ご参考になると幸いです。
He incurred his boss's enmity towards him because his English was better than his boss's.
He knew his boss was bitter towards him because his English was better than his boss's.
enmity を使うと、とてもかたい言い方になりますが、次のように言えます。
ーHe incurred his boss's enmity towards him because his English was better than his boss's.
「彼は上司より英語が上手だったので、上司の反感を買った」
to incur one's enmity で「反感・恨みを買う」
次のように言った方が、もっと自然な感じになります。
ーHe knew his boss was bitter towards him because his English was better than his boss's.
「彼は上司より英語をが上手だったので、上司が彼のことを恨んでいるのを知っていた」
to be bitter towards ... で「…に対して恨みを抱く・辛く当たる」
ご参考まで！
アメリカ合衆国 
カナダ 
