The arrogance of many ignorant disciples of science

Yesterday, at 6 am with an empty stomach and a headache torturing me to insanity, I tried to have an argument with a pretty interesting young girl over the internet. Basically, she tried to deny the right of existence for Christianity because of illogical, contradictious aspects within the own world of Christian beliefs. She brought up the example of Christmas and the probably wrong dating and concluded since the date's wrong anyway, people shouldn't celebrate it in the first place. Still to believe that the written and colloquial sources hold true, "to have faith" in it, would be naïve and irresponsible. Actually, that argumentation of hears bore two fallacious implications: The first is that concepts shall be (completely) abandoned once they're proven wrong and second that the science are superior to non-scientific concepts.
However, there are several questions to confront the girl's radical logical reasoning: What's the problem with the wrong date? What to be thought about the fact that the character of Jesus Christ is actually getting substituted by the one of Santa Claus - who's supposed to be worshipped on December 6? If we're supposed to abandon Christianity because of that inconsistency - what about New Year? On the one hand, Western New Year is based on the Gregorian calendar which again is orientated on Christian holidays. On the other hand, astronomy gives evidence that the revolution of the earth takes longer than 365 days - and an additional day for every fourth year doesn't level out the gradually increasing temporal distortion. I've given two arguments of which the first unveils a scientific concept orientated on religious concepts and the second that even our scientific concepts are imperfect.
The point is that every concept is deducted from a limited set of observations and eventually faces contradictious evidence. There's the claim of (social) sciences that it holds higher value because of its principles of falsification, that theories can't be proven right but only wrong. This means that scientific concepts don't risk becoming dogmatic. That's also what the girl was playing at when she tried to distinguish between religious and cultural theories. However, just as that distinction is based on a categorization in Western social sciences, scientific concepts only exercise the principle of falsification within the system of scientific methods: If you want to criticize time measurement, you have to make an examination according to scientific methods and measures. Therefore, any concept, any theory - may it be religious, cultural or scientific - is based on deliberately chosen assumptions, theorems, which to question is simply no use. Thus, you cannot prove a whole school of theories wrong, but just sub-theories in it. And it that case, the different Christian schools have certainly led various conflicts, arguments which resulted in changes. And as all those schools are Bu lt on the principles of Christianity, Christian principles obviously must seem completely logical to them.
Therefore, the first two conclusions of that little argument were that first, every theory is normative at its core - even science, and that second, there's no use in discussing between different schools of theories.
However, there was a third, most crucial mistake in the girl's argumentation: She herself forgot about the normative character of science and considered as "real" and "true". Only because of that, she dared to question the Christian belief with system-extrinsic arguments. [work in progress]