（よ）うとしない details

write + let's + won't do

kakou to shinai

won't do; refuses to even try — the absence of an act blamed on the subject's will

meaning: won't write

うちの子こ、野菜やさいを食べたべようとしないんだよね。

uchi no ko, yasai o tabeyou to shinai n da yo ne.

Our kid just won't eat vegetables. casual

何度なんど説明せつめいしても、彼かれは自分じぶんの非ひを認みとめようとしなかった。

nando setsumei shite mo, kare wa jibun no hi o mitomeyou to shinakatta.

However often I explained, he would not admit he was in the wrong. neutral

Examples

won't do; refuses to do — the speaker watches someone decline to even attempt the act, usually with impatience

うちの子こ、野菜やさいを食たべようとしないんだよね。

uchi no ko, yasai o tabeyoutoshinai n da yo ne.

Our kid just won't eat vegetables. casual

何度なんど説明せつめいしても、彼かれは自分じぶんの非ひを認みとめようとしなかった。

nando setsumei shite mo, kare wa jibun no hi o mitomeyou to shinakatta.

However often I explained, he would not admit he was in the wrong. neutral

息子むすこは最近さいきん、部屋へやから出でようとしません。

musuko wa saikin, heya kara deyou to shimasen.

Lately my son won't come out of his room. neutral

彼かれは僕ぼくの話はなしを聞きこうともしなかった。

kare wa boku no hanashi o kikou to mo shinakatta.

He wouldn't so much as listen to me. neutral

再三さいさんお願ねがいしておりますが、先方せんぽうは交渉こうしょうに応おうじようとしません。

saisan o negai shite orimasu ga, senpou wa koushou ni oujiyou to shimasen.

We have asked repeatedly, but the other party will not come to the table. formal

ようとしない — the form written out — よ turns up after ichidan and irregular verbs (食たべようとしない), while a godan verb gives 〜おう instead (行いこうとしない).
ようとはしない — は sets the refusal against everything else the subject did do — 聞きこうとはしなかった says he was there and busy, but would not listen.
（よ）うともしない — と＋も stacks the reproach — 見みようともしない "wouldn't so much as look".

Almost always said of someone else — of oneself it turns into 〜たくない or
〜ない. A machine that stubbornly will not work takes it too:
エンジンがかかろうとしない。

もしない
〜もしない denies one minimal act that was expected of the subject (見みもしない, didn't even glance); （よ）うとしない denies the ATTEMPT behind it, so it accuses the subject of unwillingness rather than of an omission.
たがる
たがらない reports an observed lack of DESIRE and so needs a sentient subject (×エンジンがかかりたがらない); （よ）うとしない denies the ATTEMPT instead, which is why a stubborn machine takes it (エンジンがかかろうとしない).

（よ）うとする
Not the plain negative of "try" — （よ）うとする narrates one attempt or an imminent event (日ひが沈しずもうとしている), while （よ）うとしない reports a standing refusal, and the imminence sense has no negative counterpart at all.