Like ～
ようと思う 'I think that I shall do (A)', ～ようとしない is a combination of a verb that has been grouped with the
auxiliary verb う (or
よう), followed by the
case marking particle と, and then another verb. In this case,
する. ～
ようとしない is often translated as 'shall not (A)', but with emphasis on a lack of effort, or willingness.
彼（かれ）は怒（おこ）っているから、誰（だれ）の話（はなし）も聞（き）こうとしない。
Since he is angry, he is not willing to listen to what anyone has to say.
家（いえ）になかなか帰（かえ）ろうとしない。
He isn't quite trying to go home. (It doesn't seem like he is going to leave anytime soon)
As ～ようとしない implies a lack of effort, this expression is usually quite negative, and mostly refers to other people, rather than the speaker themselves. If ～ようとしない were used to refer to the speaker, it will come across as 'I shall not do (A)', which would sound very abrupt/potentially rude. If speaking about yourself,
ようと思（おも）わない may be used instead, meaning 'I don't think I shall do (A)', or 'I think I shan't do (A)'.
自分（じぶん）から買（か）って食（た）べようと思（おも）わないけど、誰（だれ）かに貰（もら）ったら食（た）べるかも。
I don't think I would eat it if I had to buy it myself, but I might if someone gave it to me.
私（わたし）は性格（せいかく）を変（か）えようと思（おも）わない。
I think I shan't change my personality.