Why is consistency described as a "minimal requirement for truth"?

Because contradictory claims can't all be true — so consistency is necessary for truth, though far from sufficient for it.

Consistency (Konsistenz) means agreement — among your thoughts, your words, and your deeds. It comes in two forms: logical consistency (your claims don't contradict each other) and practical consistency (you act as you say).

It's a minimal requirement because failing it is fatal but passing it proves little: if two of your beliefs contradict, at least one must be false, so inconsistency guarantees error. But being consistent doesn't make you right — a perfectly self-consistent set of beliefs can still be uniformly false. Consistency rules out one way of being wrong; it doesn't deliver truth.