Why is there a squeeze on your availability thee days?
To give up something means to stop doing that thing.
"Paul has given up smoking as it was causing him health problems."
'Availability' is referring to how easy it is to get something. If there is 'little availablilty' then that item is in very short supply.
A squeeze is a reduction or limit on something. a reduction or limit:
"The squeeze on profits in the oil industry has led to thousands of redundancies."
"The squeeze on local spending means that many services will have to be cut."
"To give up something"とは何かをあきらめるという意味になります。
【例】
"Paul has given up smoking as it was causing him health problems."
（ポールは健康に害が及んできたので喫煙を辞めまています）
'Availability' とは何かを簡単に手に入れることが出来る、利用することが出来る、と言う事を言います。
もし何がが 'little availablilty' と言う状態だったら、その商品は供給不足だという事になります。
"squeeze"とは絞り出すこと、と言う意味になります。
（削減、限界）
【例】
"The squeeze on profits in the oil industry has led to thousands of redundancies."
（石油業界で利益の絞り出しをしたら多くの過剰が起こった）
"The squeeze on local spending means that many services will have to be cut."
（地元自治体の支出の絞り出しをするという事は多くのサービスが削減されるという事になる）
It’s not been possible to book your lessons recently. Are you on holiday or are you not working anymore?
first example has subject you between helping verb have and main verb stopped teaching creating a nice verb phrase.
Second example has statement at the front setting the scene for the question that follows.
I noticed you have no more class openings for the future. Are you going to stop being a teacher? Will I be able to book classes with you again in the future?
English teachers may not offer future openings on their calendar for a number of reasons. You may want to know if they are stopping permanently or taking a short break. Maybe the teacher is going on a vacation for a week so their schedule has no openings. Or maybe the teacher works another job and must wait for that schedule before creating openings for teaching English.
I noticed you have no more class openings for the future. Are you going to stop being a teacher? Will I be able to book classes with you again in the future?
（これから先授業を予約できる日がないのですが、先生をやめるのですか。この先、またあなたの授業を予約することはできますか）
先生の予定表に授業を予約できる日がない場合、これはいくつかの理由が考えられます。本当にやめてしまうのかそれとも短い休暇を取るだけなのか気になるかもしれません。
もしかすると、一週間休暇を取るので予定表に空きがないということかもしれませんし、あるいは別の仕事をしていて、そっちのスケジュールを待たないと教えられる日が決められないという可能性もあるでしょう。
"Will you still open teaching slots?"
This question is asking whether the teacher/tutor will still be 'opening' teaching slots, this is mainly used or online teaching.
open is to make something available.
'tutoring' is very similar to teaching, to tutor someone is to teach them.
"Will you still open teaching slots?"（これからもレッスンをしますか）
→これは、これからも予定表に予約できる日を載せるのかどうかを尋ねています。これは主にオンラインレッスンで使われます。
'open' は「利用できるようにする」という意味です。
'tutoring' は 'teaching' と非常によく似ています。'to tutor someone' は 'to teach someone'（教える）です。
"Are you still going to be teaching?" This asks the teacher if they are still going to continue as a teacher and keep giving people lessons.
"Are you retiring?"
"retiring" Is when you leave your job because of your old age.
"Are you still going to be giving lessons?" This asks the teacher to tell you if they will still be teaching lessons in the future.
"Are you still going to be teaching?"
（もう教えないんですか？）
これは先生にレッスンで教える事を続けるかどうか尋ねる表現です。
"Are you retiring?"
（退職するんですか？）
"retiring"とは年を取ってきたために仕事を退職することを言います。
"Are you still going to be giving lessons?"
（まだレッスンを行うつもりですか？）
これは先生にまだレッスンで教えることを続けのかどうかる尋ねる表現です。
I see that your lessons are no longer available. Are you going away?
*Are you giving up teaching?
To give up on something means to stop doing something for a specific reason.
For example: "The teacher gave up her job."
*I see that your lessons are no longer available. Are you going away?
Sometimes a teacher may close their availability because they maybe going on holiday or retiring from teaching. Therefore you can ask the teacher and they can share with you the reason why.
*Are you giving up teaching?
To give up on somethingというのは、特定の理由で何かをやめることを意味します。
【例文】
"The teacher gave up her job."（先生は仕事をやめた）
*I see that your lessons are no longer available. Are you going away?
先生が休暇をとったり教えることから引退するために予約ができないようになることもあります。ですから、先生に尋ねれば、理由を教えてもらえるかもしれません。
Are you still teaching? I am unable to book your class.
Are you no longer giving lessons? I see you are not available to book.
"Are you still teaching? I am unable to book your class." This gives a direct question to your online teacher. By first asking the question you are discussing the issue at hand and then backing your question up by giving a reason to why you are asking. It also shows the teacher that you are trying to book her class but have had a problem doing so.
"Are you no longer giving lessons? I see you are not available to book. " - This question is a gentle way of asking if the teacher has quit. You then give reason to why you are asking this question by saying that your teacher is not available when you have tried to book their class.
"Are you still teaching? I am unable to book your class."（まだ教えていますか。
あなたの授業を予約できません）
→これは先生に対して単刀直入に聞いています。まず自分が疑問に思っていることを伝えて、それからその理由を説明しています。「授業を予約したいができない」と伝えています。
"Are you no longer giving lessons? I see you are not available to book."（もうレッスンはやらないのですか。あなたの授業を予約できません）
→これは「先生を辞めたのですか」の遠回しな言い方です。「あなたの授業を予約することができない」と、辞めたのではと思う理由を伝えています。
Do you no longer teach lessons?は「もうレッスンはしないのですか？」という意味です。
no longerは、「もはや～ない」という意味で、この場合のように、「以前はやっていたことを、もうやらなくなる」ような場合に使えます。
例）
She is no longer interested in me.
「彼女はもう僕になんか興味ないよ」
We can no longer afford to pay for the service.
「私たちにはそのサービスにお金を出す余裕など もはや ありません」
以上です。少しでも参考になれば幸いです(*^_^*)
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