If I believe the Bible to teach one thing and man can reasonably show that what I believe the Bible is teaching is false then I ought to reconsider what I had believed.
For example, I used to believe that God created the earth out of nothing according to Genesis 1:1. But man has shown that the earth is much older than the idea of creation out of nothing as is supposed by Gen. 1:1
So, taking another look, I see that God never says that he created the earth out of nothing in Gen 1:1. Rather, I see that the earth actually already existed in Gen 1:1, just not in the form we know it today.
However, some people want to hold the idea that Gen 1:1 is speaking of the earth being created out of nothing and therefore they conclude that the days of creation are not literal days but very long periods of time. i disagree.
Then there are still others who hold that Gen 1:1 is telling us that God created the earth out of nothing and yet the days are literal 6 days. So, they have a problem with science.