請問 Debra will have a meeting ___ an hour later. 空格答案是half，為什麼不可以用at?

To Deborah:-
for a period of time 60 min. is not a point of time.
for a period of time half an hour=30 mins.is a point of time beforehand for the time being;also it is more idiomatic to say personified as Deborah to you.

因為an hour later（指的是一個時間量，而非時間點）即可當副詞使用，不能加介系詞at。介系詞at是用在有時間點的狀況，如：at 6 o'clock。
at a certain point of time =在某個時間點時

for an hour=為期一個小時。這時會用到介系詞for (how long)。

half an hour =半小時
half an hour later =半小時之後

Debra will have a meeting half an hour later.
Debra將會在半小時之後開會。

*請留意“later"那個字, "half an hour”=半小時。

台灣的英語教學因這種問題阻礙了學生的英語能力。第一，這問題的重點是什麼? 如果是中翻英填充題，無可厚非。選擇題，我也想問為什麼不能選 at?

如果沒有前後文單純這句話，填入 "at"，是多此一舉。但因此讓學生以為不能填介系詞，這後遺症將是長期難以回復。
Debra will have a meeting ___ an hour later.

如果你要表達一個明確的時間點時，同時有前文所提及的時間參照點，就可以使用 at an hour later.
He got off airplane at 9 AM and scheduled a meeting with Mr. President at an hour later.

1.) The lockdown was later lifted at an hour later after the scene was declared safe by police.
http://nypost.com/2016/10/18/several-students-shot-outside-san-francisco-high-school/

2.) But despite medics' best efforts, she died at an hour later, officials said
http://www.dailymail.co.uk/news/article-2766825/Ohio-college-student-killed-falling-tree.html

3.) His second meal is a small protein drink at 9 a.m. Manganiello has a second round of breakfast at an hour later.
http://www.ibtimes.com.au/joe-manganiello-fitness-secret-low-carb-paleo-diet-crossfit-workout-1371863

My explanation of why using half instead of at in that sentence. It is because of "half" which will indicate the time i.e. half an hour or 30 minutes. Yip