First of all circular reasoning is a logical fallacy. It's kind of funny that someone claims you can use logic to disprove logic.

But more importantly, this happens to be true. Logic cannot prove itself true, but logic never proves anything true -- that isn't what it does.

Logic, rationalism, the scientific method -- whatever you want to call it -- does not prove anything true.

A scientific theory is never regarded as a pure truth, but as a model for how something generally works. Testing the model doesn't ever prove it to be true because there is no such thing as an absolute truth. The best you can do is show that it works.

For example, Einstein had a theory that spacetime is warped by mass, and that was part of his model for how gravity worked. He used to model to make a prediction, that during a solar eclipse a star which we all know should be in one point in the sky would appear to be in another point in the sky because the light from that star would follow a bent path through spacetime caused by the distortion of the sun's gravity.

He used a model to make a prediction. The fact that his prediction came to fruition doesn't prove that his model was true, but demonstrated that it works for making certain predictions. If his prediction had not occurred it would have falsified. In fact, Einstein's model is now known to be imperfect, just as Einstein's discoveries lead us to understand how Newton's model was imperfect (as demonstrated by the orbit of Mercury which cannot be explained by Newton's model, but is predictable using Einstein's theories of relativity.)

Logic doesn't show us what is true so much as it shows what is not true, or, more aptly, not a functional or reliable model for making predictions.

The problem with this argument is that he is looking for absolute truths and you are trying to say that science, logic, and rationalism are absolute truths in the way religion has always tried to be. They aren't.

The strength of rationalism isn't that we have absolute truth but that we have insight into what works and the ability to reserve judgment when we don't know. The strength of logic and rationalism is that it allows us to discard ideas that no longer work and replace them with ideas that work better instead of adhering to orthodoxy even when it is obviously flawed.