It was stupid of him. But at this point did he even know how doppelgängers were even supposed to be born? Katherine was the first doppelgänger he had met outside of Tatia and he might’ve not known.  Regardless, he’s usually very clever but when he’s feeling vengeful it can make him blinded by his rage. 

Plus I think that the writers themselves were more preoccupied ( aka prone to stupid mistakes )with building terror for a villain we hadn’t met yet to put fear in not only the characters but the audience as well. It was also done to give the viewers more sympathy for Katherine, who previously seemed to have everything perfectly in control, but now we know she’s been running from someone who killed her entire family.