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Nothing annoys people more than breaking a promise.
Literal
Promise [obj-を] break thing-[extent-ほど] person [obj-を] make-unpleasant thing [topic-は] not-exist.
The superlative pattern ~ほど~ものはない ('there is nothing that X as much as Y') is a productive way to make superlative statements in Japanese. Literally: 'there is no thing that makes people as unpleasant as breaking promises.' 不愉快にする is a transitive idiom — 'make (someone) feel unpleasant' — using に + する to produce an affect.