His argument was riddled with holes and fell apart by itself.
Tips
history
Attested in the Jin-dynasty 《晋记》 as 不攻而自败 and in Tang writings as 不攻而自破. The image is a fort so weak it crumbles without a siege, extended to any claim whose weakness is self-evident.
usage
Subjects are usually abstract: 谣言 (rumors), 论点 (arguments), 谎言 (lies). Typical pattern: [evidence] 一出,[claim] 不攻自破. The positive twin: 牢不可破 (unshakeably firm).