How are market rallies "fueled by sellers", and market sell-offs "fueled by buyers"?

I am looking at Trading the Measured Move by David Halsey. In chapter 5 Using Multiple Time Frames to Trade, section Trading the Trend, page 85:

Why Do Markets Continue to Make New Highs?

Markets continue to rally because they are fueled by sellers at highs. Markets will stop making new highs when the very last of the bears turn bullish right at the highs. Without sellers at highs, the market has no fuel to push through to new highs. This is where we get the saying, "The market climbs a wall of worry."

Similarly, the book’s subsection Why Do Markets Continue to Make New Lows? claims that market sell-offs are fueled by buyers at lows.

These explanations in the book contradict my understanding of how markets work. From my own understanding of supply and demand, markets continue to rally because they are fueled by buyers (willing to pay higher prices) at highs, and markets will stop making new highs when the very last of the bulls turn bearish (i.e. unwilling to pay higher prices) right at the highs. The author’s explanation appears to contradict my understanding.

Is there anything I’m missing? Am I wrong? If so, could you please explain what the author is trying to convey?