*I owe it to you that my English is good.- If you "owe it to someone" it means that you have something because of someone. Therefore in this case it means that your English is very good because how good the teacher is at teaching that has helped you to speak fluently in English.
*It's all thanks to you.- This means that you feel like the teacher teaches you in a way that makes it easier for you to learn English.
*I owe it to you that my English is good.
私の英語が上手なのは先生のおかげです。
"owe it to someone"とは、誰かのおかげで何かを得た、もっているという意味です。ですので、この場合、自分の英語が上手なのは、先生が教えるのがうまくて、手伝ってくれたからという意味になります。
*It's all thanks to you.
全てはあなたのおかげです。
これは、先生の教え方が学び安い環境を作ってくれたということを意味します。
Both of these statements admire your teacher and show that you appreciate them and appreciate their teaching. This is because it helped you to acquire and develop your English. It shows that you like the way they teach you and the methods they use to do so.
My English is improving thanks to your dedicated tutelage
My English improvement is all down to you!
The first sentence is more formal than the second, but both convey your appreciation of your tutor's input. In the UK, indirectly thanking someone is usually preferable and less embarrassing than saying 'Thank you for being a great teacher!" directly.
１つ目の回答は２つ目に比べるとよりフォーマルですが、どちらも先生の教え方がいいことに対して感謝している、という事を伝えることができます。
イギリスでは、'Thank you for being a great teacher!"（とてもいい先生でいてくれてありがとうございます！）と直接的に感謝の気持ちを表すよりも、間接的に表現するほうが恥ずかしさも減り好まれます。
You show your gratitude and thanks to your teacher by telling her: I am improving greatly with my English because I have a great teacher like you.
"I owe it to you" is also a common expression used in the U.S. to express thanks to someone for the efforts to help you succeed.
感謝の気持ちを先生に伝えたい場合は以下のように言うといいでしょう。
I am improving greatly with my English because I have a great teacher like you.
ーあなたのような素晴らしい先生のおかげで、私の英語は上達しています。
I owe it to you ーあなたのおかげです。（これはよくアメリカで聞くフレーズで、自分が成功したことに対して「の手助けのおかげです」と感謝の気持ちを表したい場合に使います。）
日本 
南アフリカ 
イギリス 
アメリカ合衆国 
