あまり and とても, what's the difference?
When I was doing N5 exam exercise, I see the following question

このケーキは( )おいしいですよ
A. あまり
B. とても

What is B correct but not A?
Even some Japanese people use A such as this guy.
He wrote “最近はあまりおいしいと思わなくなりました” on his blog.
http://www.tripadvisor.jp/ShowUserReviews-g298560-d1667435-r180921998-Gensaku-Sapporo_Hokkaido.html

Question

あまり and とても, what's the difference?
When I was doing N5 exam exercise, I see the following question

このケーキは(         )おいしいですよ
A. あまり
B. とても

What is B correct but not A?
Even some Japanese people use A such as this guy.
He wrote “最近はあまりおいしいと思わなくなりました” on his blog.
http://www.tripadvisor.jp/ShowUserReviews-g298560-d1667435-r180921998-Gensaku-Sapporo_Hokkaido.html

Answer

とてもis used for affirmative, and あまりis used for negative sentences.

あの映画はとてもおもしろかった。
このお菓子はあまりおいしくない。
あの子はとても優しい。
あの服はあまり私の好みではない。

As for the sentence that you mentioned, "最近はあまりおいしいと思わなくなりました。"
he's saying that he doesn't think that tastes as good as he used to think anymore lately, which is a negative sentence.

I imagine it's very complicated till you get used to using those words.
Hope this explanation helps!

Answer

あまり～ない（or ありません） is a set phrase.

最近はあまりおいしいと思わなくなりました。
↓
思わなくなりました is an inflected form of 思わない.
あまり～と思わない
"あまり"～思わ"ない" The set phrase is used.