NO he picks on him because he doesnt get why Deku wants to be like almight when he has no qiurk so it makes Bakugo mad so he takes all his anger out on Deku , and btw Bakugo wants to be like almight so he is jealous
i actually watched the show and he got his qiurck from all might but before thats he was qiurkless and when deku was younger he always fallowed bakugo and yeah...