Atheism is irrational.

[Primordial Bisque]

Whatever is rational utilizes either the senses, the intellect or both.

Atheism cannot deny God by using senses. For, to deny something by the use of senses is to search the whole physical reality, just as ruling out that there's no alien is to search all that is searchable which is impossible for us humans. But God, by demonstration of His effects, shows that He is beyond physical reality. Hence, it is the more that God can't be denied by the senses.

Atheism cannot deny God by the intellect. For, whatever we can deny by the use of our intellect, must be defined, just as we deny circle things as square, for the definition of circle is different from the definition of square. But, God can't be define, because if He has definition, He can't be God, because by demonstration of His existence through His effects, He is necessarily Boundless. Hence, God can't be denied by the intellect.

Therefore, if to be rational is able to use senses and our intellect, and that God can't be denied both by the senses and intellect, then atheism is necessarily irrational.

If god does not have any direct definition, or exist within physical reality, then it does not have any real identity and is equivalent to absolutely nothing. It is a vague concept, contingent upon natural reality in order for you to imagine it exists. It's a null-entity, unnecessary, and grows increasingly useless as we discover, learn, and understand our universe.

The next time you want to preach about rationality, try to ease up on the mumbo-jumbo. It hurts your case.