A rational argument (or belief) is one based on good reasoning and logic.
Does it matter to me? Yes. If you are going to go around saying your belief is "rational & convincing" when you admit that the reason you believe it is because it "feels right" or because you "like it".
I don't care if you change your beliefs or not; I'd prefer you changed your way of forming your beliefs. I don't believe things because I like them (indeed, I have some beliefs I don't like), or because they "feel right". I believe things because they have logical reasoning backing them up.
Does it matter to me? Yes. If you are going to go around saying your belief is "rational & convincing" when you admit that the reason you believe it is because it "feels right" or because you "like it".
I don't care if you change your beliefs or not; I'd prefer you changed your way of forming your beliefs. I don't believe things because I like them (indeed, I have some beliefs I don't like), or because they "feel right". I believe things because they have logical reasoning backing them up.