Were the Prophets, peace be upon them, mistaken for being shepherds, and does shepherding contradict infallibility and patience?

The questioner's intent is not entirely clear. However, if their purpose is to suggest that the wisdom behind prophets tending sheep was not to accustom them to patience, then this is incorrect. Tending sheep requires patience and gentleness, and it teaches them the management of people. Just as they patiently tend the sheep, gather them, repel their enemies, and understand their natures, so too do they patiently guide their nations and comprehend their varying dispositions. Sheep were specifically chosen due to their weakness, their tendency to scatter, and their quick submission. This was a training for the prophets in governing their nations, moderating their natural intensity, refining them from innate injustice, and accustoming their hearts to humility and solitude. It has been reported that tranquility and dignity are found among the people of sheep, and that mingling with animals affects the soul.