Evan TessellNikoli's history identifies symmetrical clue arrangements as a design choice it adopted in 1986. The visual balance of a clue pattern is interesting to inspect, but the pattern is separate from the digits a solver must place.
In a grid with half-turn rotational symmetry, a clue at r1c2 has a matching clue location at r9c8. The values at those two locations do not need to match. It is the occupied positions that correspond when the page is rotated, not necessarily the printed digits.
You can test the pattern on an empty coordinate diagram. Pair r2c4 with r8c6, then pair r3c9 with r7c1. The center cell r5c5 maps to itself. This exercise describes geometry and does not place any new Sudoku values.
During a solve, avoid concluding that a blank must copy the value in its visually paired cell. Unless the instructions explicitly add such a rule, the normal row, column, and box restrictions determine its value. Symmetry may help the page look orderly while providing no additional logical constraint.
If you examine several puzzle pages, record the clue positions separately from the clue values. That lets you compare layout without confusing appearance with correctness or difficulty. A puzzle can have a balanced pattern and still require careful reasoning. A less symmetrical arrangement can also obey every classic Sudoku rule. The design is something to appreciate; the deductions still need their own evidence.