Recently I have started reading Bourbaki's Theory of Sets on my own. Regarding one of the explanations of a concept when I went to a Professor of our college, he asked me why I was wasting my time reading a book which contains so many pitfalls. Besides, he also told me that Bourbaki's treatment of Set Theory is wrong. When I asked him about examples, he told me that he thought I would be able to find it myself.
Now this is something that is highly contradicting because here in D. Miller's answer I found that,
...Bourbaki is very far from being suitable for everyone. That said, if you're looking for a reference that's axiomatic, super-abstract, and works in greatest possible generality, and is also crystal clear and careful, Bourbaki is the place to go. ...
And this contradicts the expression I got from my professor. Besides, I himself wasn't able to find out any 'pitfall' in the book so far.
Is there really anything wrong with Bourbaki's Set Theory?
Update
Though Asaf Karagila was very patient with me and answered all my queries, I will be very glad if someone who has gone through Bourbaki's Theory of Sets answers it in detail.
The fundamental problem with Bourbaki set theory is that they bury the axiom of choice at the level of the syntax of the formulas and not at the semantic level (as an axiom), making the development of different set theories (ZF with or without AC,...) impossible within the frame they chose. A really symptomatic example is the absence of category theory in their treatise, because they would need the Grotendieck-Tarski set theory (ZF + an axiom on universe) to be fully rigorous.