用 takes up the means you act WITH (用筷子 = with chopsticks); 把 takes up the object you act ON (把飯 = the rice itself). The chopsticks are the tool, the rice is the target.
用 marks a tool; 跟 marks a person you act alongside. 用他 would mean 'using him', 跟他 means 'with him'.
instrument after the verb: 他吃飯用筷子 → 他用筷子吃飯
verb dropped, 用 left stranded: 他用筷子 → 他用筷子吃飯
marking a companion with 用: 我用朋友去 → 我跟朋友去
English puts 'with chopsticks' after the verb ('eat with chopsticks'); the instrument in Chinese comes before the verb, so learners strand it at the end.