"convincing case" means presenting evidence or argument that is persuasive and leads others to believe or agree with a certain point of view or idea. Full definition
All in all, I don't see a very convincing case for deep ocean sequestration of heat. (judithcurry.com)
She makes a very convincing case for attachment theory taken further into how it plays out in adult relationships. (amazon.ca)
He attacked active trading and made a pretty convincing case against being able to profit over the short - term by stock picking. (moneysmartsblog.com)