I think it has to do with his obsession with Sisko, his need to keep up with and hopefully outdo the one man who he's fixated on as his rival. Some fans have expressed their dissatisfaction with Dukat's blaming Sisko for everything (even blaming him instead of Damar for Ziyal's death), but to me it makes very real sense in a twisted, irrational way: Sisko has everything Dukat wanted, and is stealing Dukat's life from him; therefore, Dukat must become more like Sisko. Sisko succeeded where Dukat failed; part of that was by having the support of the Prophets. Dukat therefore will now be emissary for his own group of wormhole aliens, and readdress the failing.
We could also say that briefly hosting a pah-wraith in Tears of the Prophets
changed him entirely, made him a puppet of the pah-wraiths, but that cheapens his character to such an appalling extent I'd much rather explain his actions in season 7 in terms of his pre-existing personality, which I think it can be.