a Particle
subject
Object of emotion
Where you'd consider a word transitive in Fnglish, if it is about emotion you consider something an object of emotion. This is also why so many 形容詞 exist that English uses verbs for.
私はお父さん~~を~~心配です。 私はお父さんが心配です。 I am worried about my father
野菜が好きです I like vegetables.
https://www.wasabi-jpn.com/japanese-grammar/japanese-adjectives-with-particle-ga/
Object of potential
When using adjectives that describe potential such as 苦手 = "bad at (...)" or 下手 = "unskilled in", you use the particle 「が」to express the object of potential
私が数学が苦手です I'm bad at mathematics.
私は日本語が上手い外国人です I'm a foreigner (who is) good at japanese.
This is not the case when it's related to attitude and eligibility: then it goes with に
e.g. attitude
- 新設
- 丁寧
- 厳しい
- 冷たい
Eligibility
- 強い (strong againts ...)
But
See が. indicates a contradiction; 'but'. same meaning as けど. It is a literary variant, and is more #formal however.
デパートに行きましたが、何も欲しくなかったです I went to the department store, but there was nothing I wanted.