That's not true, two opposiong positions can certainly both be rational.
Suppose one man has lived his whole life on a boat, in the middle of the ocean, and has never seen dry land. In the absense of other evidence, it would be rational for him to assume that the whole world is covered by oceans.
Suppose another man has lived his whole life in the desert, and has never seen any body of water. In the absense of other evidence, it would be rational for him to assume that the whole world is covered by dry land.
If a person is "irrational", it means they do not determine their positions using rational thought. This is a much stronger statement than to say that a person is incorrect, or even that their reasoning is faulty. It is to say they do not base their ideas on reason at all.
I don't think you're irrational, even though I think you are wrong. Your thought processes seem to me to be quite rational.