The Dalish racism against City Elves had to have played a part there. And in all fairness, she does have a point when she says that Andrastianism and the Dalish religion can't both be true, because monotheism is the bedrock tenet that the Andrastian faith is based upon. For all her flippancy about things, Sera's faith is too important to her for her to be able to set it aside, and when she was growing up she found a place in the faith of the Chantry that the faith of the Dales never offered her.
So the sad thing is, if the Inquisitor chooses to profess a belief that what they were told in the Temple of Mythal was true, she's making an ultimatum that Sera has to abandon the faith that was her one source of comfort and meaning for too much of her life. It's tragic, but it's also powerful storytelling.
Ok, this thread is really derailed, but I have to respond to this

You're wrong. Dalish religion can be reconciled with andrastianism pretty easily. First of all, there is nothing in Dalish religion that contradicts existence of Maker. Elven gods are consistently described as being children of the world. They're not some beings from elsewhere - they were born of this world and never had complete knowledge of it either. The legends we have about Dirthamen and Falon'Din have them discovering nature of death and the Fade. Legends about Andruil and her journeys to the Abyss speak of her pride and lack of understanding of some aspect of the world leading to disastrous consequences. Ghilan'nain is originally an elf granted position as a god... Basically, elves see their gods as powerfula nd benevolent (now more than in times of Arlathan) but not infallible. They're teachers, to an extent also parents or older siblings, but they're not as alien to elves as Maker is to humans. And here is the difference: if those two religions were to be reconciled, you would find that they don't really compete against each other. Most likely Andraste would end up as more-or-less peer to elven pantheon - she's indeed much closer to elven definition of god than Maker, the latter being a different kind of being altogether - not referenced in elven myth but neither denied by it.
Also, as for Sera herself - note that it's her who starts the conversation and demands elven Inquisitor to denounce whatever they saw in Temple of Mythal. And no, she doesn't take any dodgy "I don't know" for answer, she wants to hear Quizzy denouncing everything. It's not Quizzy setting any ultimatum, she doesn't require Sera to accept anything. The only one making demands there is Sera.