It was a losing situation from the very beginning going to Big Mom to tell her he wants to leave. He knows what people that defect get but he goes to ask for her....blessing I suppose to leave. If she refused to just let him go he knows there's gonna be punishment. He runs away from the punishment and just defects anyway. The obvious thing would be just defecting without telling her but he ran away from a punishment he knew would come by his actions. He didn't oppose her to her face, he just backed out, ran away, and opposed her behind her back.
He didn't run, he refused the offer. Which makes 100% sense.
He asked big mom face to face if he may leave. She said 'yes if you try the roulette'. The roulette is a 100 % death guarantee as stated by brulee.
So if he wants to leave he has to die.
The reason why he wants to leave is he wants to join luffy and accompany him and help him achieve his dream.
If jimbei is dead he can't help anyone, and nobody gains anything from his death. It is completely pointless.
So the next best thing to do is to betray big mom and just help luffy, because fighting her would be ridiculous since nobody who isn't a monster tier big shot can win a 1v1 vs big mom. He puts himself and his crew in danger just to help luffy by starting a riot without hiding it.
He just starts a fight with a yonko when he had no problem of being in danger or anything before. This is the definition of being brave, the total opposite of being a coward.
Luffy, Bege and co. have a plan for the tea party. None of them is planning to fight big mom 1v1, they just plan to attack from ambush.
Are they all cowards now?