IPA: /ˌʌn.kənˈvɪn.sɪŋ.li/
KK: /ʌnˈkənˌvɪnsɪŋli/
In a way that does not persuade or make someone believe something is true.
She explained her point unconvincingly, leaving everyone confused.
Unconvincingly → It is formed from "un-" (meaning not), "convincere" (from Latin, meaning to conquer or overcome), and "-ingly" (a suffix used to form adverbs). The word means in a manner that does not overcome doubt or skepticism.
Think of 'not' ('un-') being able to 'overcome' ('convincere') doubt — that's why unconvincingly means not convincing.