How to understand the second rule of front door criterion?

In the Definition 3.4.1 of Pearl's causal inference book (Primer), the second rule for the front door criterion is "There is no backdoor path from $$X$$ to $$Z$$". But from my understanding, there EXISTS one backdoor path from $$X$$ to $$Z$$: $$X \leftarrow U \rightarrow Y \leftarrow Z$$. And this backdoor path is blocked by the collider $$Y$$.

Can anyone help me understand this rule? Thank you.

I can understand your confusion. In the Front-Door Criteria of Definition 3.4.1, the original text for #2 read, "There is no unblocked path from $$X$$ to $$Z$$." The book's errata changed that to "There is no backdoor path from $$X$$ to $$Z$$." I admit it's a bit confusing either way: Pearl was a little more careful in his 2009 book Causality: Models, Reasoning, and Inference, 2nd Ed. On page 82 of that book, Definition 3.3.3 (Front-Door), the second item on the list reads: "there is no unblocked back-door path from $$X$$ to $$Z;...$$"
It certainly is the case that $$Y$$ satisfies the Backdoor Criterion (Def. 3.3.1 on page 61) relative to $$(X,Z).$$ This is what enables Pearl to say, in the derivation of the Front-Door criterion, that
$$P(z|\operatorname{do}(x))=P(z|x).$$