It seems the reopeners did not read carefully, likely reading only the first
dupe link, which gave the proof of the CRT solvability criterion. The
2nd dupe link gave a very detailed example which is exactly the same as in this question, ie. the moduli gcd = 2 so reducing the system mod 2 immediately yields a parity contradiction, viz. r = r+1 (mod 2), explained in a closing comment.