eg The argument does not hold good.
eg The reason is spurious/tenuous/weak/feeble/flaccid.
but can I also say?:
-This reason/argument doesn't stand.
-This reason/argument doesn't have a leg to stand on.
I'd say that when we engage in serious discussion, we tend to address the person rather than the argument.
Your argument does not hold (water) good
Your reasoning is spurious/tenuous/weak/feeble/flaccid.
Your/This reason/argument doesn't square with reality/square with the facts.
You don't have a leg to stand on.