N3
〜ようとしない
Not willing to, Not make an effort to, To not attempt or try to, Volitional + としない
家になかなか帰ろうとしない。
He just won't go home.
Explanation
「Vようとしない」 means 'won't even try to...' or 'refuses to...'. It follows the volitional form (う / よう). It is used for other people (third person): the speaker, with annoyance, worry or criticism, sees someone stubbornly showing no intention to act, making no effort, even avoiding it: 「子どもが野菜を食べようとしない」 (The child won't even try to eat vegetables); 「彼は間違えたのに、謝ろうとしない」 (He made a mistake but won't apologise).
Mixed up with
Only for others, never for yourself: 「×私は行こうとしない」. To say you don't want to go, use 「行きたくない」 or 「行くつもりはない」.
Related patterns: 「~ようとする」 is about to do or trying to do; 「~ようとしたが」 is tried to do but got interrupted; 「~ようとしない」 is stubbornly not willing and making no effort.