The reason a concession makes the following claim stronger

The costs are real, but the alternative is worse. Read that sentence and note which half you would repeat. Concessive syntax puts the conceded point in the subordinate position and the intended conclusion in the main one, and readers reliably carry away the second.

What everyone sees

A sentence of that shape reads as even-handed, because both sides appear in it. Readers describe such writing as balanced and fair, and they are describing the structure accurately. What the structure does with the two halves is not part of the description.

What is actually happening

Linguists analysing concessive constructions have long noted that but subordinates the first clause and marks the second as the speaker’s position; the pattern is described in work on discourse connectives by Blakemore and others. Recency in comprehension favours the later clause, and studies of message order find that when a decision follows immediately, the final argument carries disproportionate weight. Balance is displayed while emphasis is assigned.

Why it stays hidden

The asymmetry hides because the concession is genuine. Nothing is misstated and the opposing point is present in the text, so a reader checking for fairness finds it. The mechanism is positional rather than propositional, and position is not what readers audit — they audit whether both sides were mentioned, which they were.