Is there any idiom or expression that would imply " It is hard to argue against such rationale"?

All of these answers accurately describe how one would claim that their own argument has no room for dispute, but your question specifically mentions the speaker admitting the other side has a point. Therefore, I would suggest the following:

• "I can't argue with that!"

• "You got me there."

• "That's a good point."

• "I'll give you that."

Inflection is important with all of these, and it might help to add "Well," or "I guess" to the start of each of them.

Case closed

per http://encyclopedia.thefreedictionary.com/case+closed

1. Said after a given question, debate, or mystery has been solved or answered. So you see, it was the dog who ate the blueberry pie, not me. Case closed!
2. The aforementioned decision, outcome, resolution, or situation is final, with no ambiguity or room for variation or amendment. The only way we'll be able to keep the company open is to undertake a 30% reduction in staff, case closed. My wife had an affair and our marriage is over. Case closed.

This derives from its usage in legal proceedings and/or police investigations. A legal or police review is referred to as a case; when a perpetrator has been identified and/or convicted, that case is settled, or closed.

Q.E.D.

Euclid's theorems state an aim, provide a logical argument and draw the intended conclusion. And then, in the latin version, add "Which is what ought to have been demonstrated" Q.E.D. Quod erat demonstrandum."

You can talk about an "ironclad/irrefutable/undeniable argument"

not able to be assailed or contradicted.