う・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

ようにする (literally, 'do things in such a way as to X') can express the idea of taking care to perform a certain action and often describes intentions or habits. 〜ようとしない conveys the opposite, not making an effort to do something. For example, 毎日野菜を食べるようにしている ('I'm making a habit of eating vegetables every day.') vs. うちの子どもは野菜を食べようとしない ('My child doesn't even try to eat vegetables.').

These two expressions are opposite uses of the same structure. Verb[volitional]とする means 'Try to do (A)' or 'Make an attempt at (A)', often with the nuance that the attempt may fail, e.g. 食べようとしたけど、無理だった 'I tried to eat it, but I couldn't.' In contrast, 〜ようとしない means 'Not even try to (A)', e.g. うちの息子は、野菜を食べようとしない 'My son doesn't even try to eat vegetables.'

Both of these use Verb [よう], the volitional form. By itself, it expresses a suggestion, e.g. 食べよう ('Let's eat'.). Combined with としない, it means 'doesn't even try to,' e.g. 野菜を食べようとしない ('He/she doesn't even make an effort to eat vegetables.'). The key difference is between making a proposal vs. showing a lack of intent or effort.