The problem is that the argument is usually framed as a form of special pleading. The "the universe must be finite, but God is infinite" argument is fundamentally flawed, since there is no reason to assume that - could an infinite thing exist - that the Universe cannot, itself, be infinite in some form and therefore not require creation.
The argument isn't one of making assertions or claims about God, but in pointing out the fallacies often evoked by such arguments. I.E: when I make this argument, I do not mean to say "The universe must be infinite, therefore God couldn't do it" or "God must be finite" or any variation on these claims, what I'm actually saying is "here is the reason why your logic is flawed and I therefore do not accept your conclusion". An infinite God isn't a problem. The problem lies in evoking an infinite being through arguing that something cannot but infinite, which is special pleading.