'ballyrag' is a compound of 'bally' + 'rag'. 'Bally' is a euphemistic minced oath for 'bloody' (used in British English), originating in the late 18th to early 19th century. 'Rag' as a verb meaning 'to tease, torment, or reproach' has been used since the 18th century.

'bally' emerged as a softened form of 'bloody' (a taboo expletive), and was combined with the verb 'rag' to form 'ballyrag' in 19th-century colloquial English, producing the meaning 'to scold or berate harshly.'

Originally, elements meant roughly 'mild expletive' + 'to tease/torment'; over time the compound came to specifically mean 'to scold or berate angrily,' emphasizing reprimand rather than light teasing.