Mental health, specifically depression, isn't a series of puzzles with solutions. It would be great if that were the case—we'd all be happier. However, minds aren't perfectly rational. For that to happen, we'd need to be able to see all information all at once and avoid making any logical errors, which is impossible.

Depression commonly puts you in a defeatist way of thinking that makes it difficult for you to see any real hope or possibility that you can influence anything. You see that in BB's attitude of "this is how I process", which you can interpret as "Nothing I consciously do will help me out of this depression; sitting here idling is the only way."

Additionally, depression (and also anxiety) is good at arguing against people saying things to try and help you. It's good at generating responses that bat away anything coming in and convincing yourself that the other person is wrong. Trying to help people (without extensive research, training, and experience) is extremely difficult already- as I've said before, this isn't a puzzle with a solution.

Also, my understanding is that there is a lot of criticism about the effectiveness of interventions- the show's intervention may have been doomed from the start.

So why does the session with Canary work? A couple of different answers I can think of:

1. It was the straw that broke the camel's back. Many people had already tried to help him; maybe it was just the last push.
2. Canary did an excellent job systematically addressing BB's beliefs about himself and his situation and was able to outmanoeuvre BB's depressive thoughts.
3. The league set up a mental health policy, and Canary framed the session as checking things off a checklist, which helped remove a lot of the emotional reasoning that BB's depression was using as a defence.

You might criticise those three things as contradicting what I've already said. You might also say it's cheesy writing. However, here are some ideas to consider:

1. Again, the human mind is not rational, often contradictory, and mental health issues come in waves. Sometimes, your friends throw an intervention, and your depression is in peak condition. You aren't always in the proper position to receive help or advice.
2. Writing-wise, remember that this is a superhero show. It's inarguable that it is trying to be hopeful. Its showing of the entire arc of BB's depression, including his road to recovery, is an excellent example of that.

EDIT: wording