That there is a spiritual world--by which I presume you mean at a minimum that there is at least one incorporeal supernatural being who has some interest in us--is an empirical claim about the nature of reality and is thus open to scientific investigation. The evidence produced so far is not sufficient to justify accepting the claim as true, all of it admits to more mundane explanations, most commonly rooted in errors of perception, logic, and interpretation.
Both sides have to provide comprehensive evidence sufficient to justify their claims, evidence that is logically consistent, coherent, and evaluated honestly and without bias. Theists have not done so. They will generally resort to the authority of scripture, some version of "there are mysteries it is not given to us to understand," or sometimes they will resort to foul mouthed and abusive bad temper, demanding respect for their unsupportable claims just because they have the label "religion" on them. Those are not legitimate arguments. It's true, for instance, that science can't prove or disprove that a supernatural being created the cosmos for some mysterious purpose of his own, but the evidence does not point that way and it's not true that believing one did necessarily deserves respect.
