Unconvincing means seeming false.
The student's excuse was unconvincing. As much as she tried to make her story sound true, it was an unconvincing tale.
A lot of the evidence against Joe Bloggs was unconvincing, so the jury acquitted him.
The antonym of convincing is unconvincing, which means not able to persuade or influence someone effectively, lacking the power to sway opinions or beliefs.
unconvincing
A character may come across as unconvincing if their actions or dialogue seem inconsistent with their established traits or background, if they lack depth and complexity, or if they are not realistically motivated in the story. Unconvincing characters may also lack relatability or fail to evoke genuine emotion from the audience.
The opposite of "convincing" is "unconvincing." While convincing refers to something that effectively persuades or influences belief, unconvincing denotes a lack of persuasive power or credibility. It describes arguments, evidence, or presentations that fail to inspire trust or acceptance.
unconvincing and confrontational
having dimensions of height and width only. In a literary sense, shallow, superficial and unconvincing characters
This may be the verb or noun "inconvenience" (a disruption or hardship).The word most closely related to convince is "unconvincing" (not plausible).
unbelievable, incredible, beyond belief,inconceivable, unthinkable, unimaginable; unconvincing, far-fetched, dubious,implausible, improbable, unrealistic; hard to swallow.
Joss Whedon
Oh, that is very tough, and a hard impression to undo. The best approach is to simply be honest all the time, even if the results will be painful. Eventually, they will catch on that you mean business and that you do not lie. Don't try arguing or trying to prove that you tell the truth; that will only come across as defensive and probably unconvincing.