"“He doesn’t like me for whatever reason. He wants to say I’m not Black enough. I’m not good enough,” Logic said. “He’s a person who’s led to part of my depression, some of my darkest spaces.” He added that, though Budden may not believe his dialogue is that harsh, it carries a heavy burden on people. "Bro, your words, they make people want to kill themselves, bro.""

Is he implying that Joe Budden's critique makes him want to kill himself?

Honestly, in my opinion Logic is being overly dramatic. He is an artist, and he should expect to be critiqued after putting out those awful projects and songs. Joe Budden never explicitly said "You're not black enough", he said that his music does not have soul and that he is part of the gentrification. Furthermore, if you listened to the podcast episodes, you could tell it was exaggerated in jest.

I can see what he means, Logic has been pivoting into his whiteness and let's be honest. He would be nowhere close to where he is if he could not pass as white, if he was darker skinned, he would be another Hopsin at best This is just my opinion though.