この場合、次のような言い方ができます。
ーI didn't really plan on becoming a teacher.
「教師になる計画を立ててはいなかった」
ーI didn't necessarily want to be a teacher.
「必ずしも教師になりたいわけではなかった」
例：
I didn't necessarily want to be a teacher, but the faculty of education was the only program I was accepted into.
「必ずしも教師になりたいわけではなかったが、教育学部にしか受からなかった」
ご参考まで！
It's not that I particularly wanted to become a teacher, but since it was the only department I was accepted into, I went to study at the department of education.
ご質問ありがとうございます。
"It's not that I particularly wanted to become a teacher,"＝「特に教師になりたいという訳ではありませんでした、」
"but since it was the only department I was accepted into, "＝「ただ、その学部にしか合格しなかったため」
"I went to study at the department of education."＝「私は教育学部で勉強しました。」
ご参考までに。
カナダ 
アメリカ合衆国 
