The above paragraph is saying there will be differences between cashflow-based and weighted average-based measures of portfolio statistics if the yield curve is not flat (and they illustrated this with an upward sloping example).
A little too mathematical for me, the way I remember it is as such:
The average of a flat line (ie flat yield curve) is a flat line. The average of different slopes (eg when you average different segments of the yield curve due to where cash flows are) is another slope. This another slope may not be the same as the slope implicit in your cashflow-based measure, hence a difference in values.
Upward sloping curve means longer term bonds have higher YTM hence lower market value.
So when you combine all the bonds into a portfolio (short-term, medium-term and long-term bonds), you get a portfolio of cash flows but where the market value is averagely lower (because of the lower-value long term bonds compared to the higher-value short term bonds). So the lower the market value of the portfolio, the higher the YTM of the portfolio (or we call it cash flow yield) compared to just a market-value-weighted-average of YTMs.
With more cash flows in the portfolio + below-average market value (small base), the portfolio duration is also higher than compared to the market-value-weighted-average duration.
You don’t expect to get through Level 3 without a fight, right?