Why does it look like an ad with a high Quality Index doesn't have a high click-through rate?

This might occur due to one of several reasons:

Because quality index is indicative of an ad’s performance relative to competing ads, even an ad with a high click-through rate might have a low quality index if competing ads have higher click-through rates.
Click-through rate can fluctuate on a daily basis. Because the displayed click-through rate is dependent on the chosen date range, any short date range might show a click-through rate that seems out of synch with the quality index. Quality index, which cannot be modified by data range, is a historical indicator that will smooth out daily click-through rate fluctuations. Quality index is updated daily based on the previous day's clicks and impressions.
Quality index is composed of both expected performance and historical performance factors. As an ad receives more impressions and clicks, the historical performance has a greater influence on the quality index.

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