Here the verb ‘to cry’ means ‘to offer for sale in the street’. Barrow-boys cry fruit: ‘Fine ripe strawberries!’ Flower-girls cry flowers: ‘Lovely violets!’ Fishmongers cry fish: ‘Fresh-caught mackerel!’ But they and others of their kind would not find many customers if they condemned their own wares – ‘Overripe strawberries!’ and so on.
By extension, to cry stinking fish is to belittle one’s own efforts; to speak unfavourably of what one has to offer to others. For example, a young author sent his first novel to a firm of publishers with a covering letter admitting that the grammar was faulty, the construction weak and the plot unoriginal, but he hoped they would accept it for publications. We wonder if they did! Of course, to go to the opposite extreme can be even worse.