Update: I've come around on MGK's part. The first part of his rap is just bravado, trying to convince her (and himself) that due to the attention that he's getting, that he's worth keeping… before it crumbles entirely, and he admits that he misses her deeply.
It then goes on to him trying to justify the toxicity in their relationship as something that just happens—according to him, happens in every relationship—trying to bargain with her, and eventually going back to drinking to forget his pain, thus trading one problematic attitude for another.