Well, that is the way it works. If I say I have a cure cancer, do I have to prove the cure works? Or does another scientist have to prove that the cure doesn't work? Of course its the former and not the latter. Why would anyone have to prove a negative? It makes absolutely no sense to try and prove a negative. It accomplishes nothing.
Actually the notion of proving that something doesn't work or is false is an element of peer review within the scientific method, but proving an initial negative claim is typically not something that is done.
Lawrence Krauss repeatedly affirms "that's how we do science".
Scientists spend a great deal of time attempting to disprove the affirmative claims made by other scientists so that all bases are covered prior to deeming a new discovery, methodology or principle sound.
The breakdown for "science" it that is demands that the scientific method of proof be utilized for a state that transcends time and space....God transcends the naturalistic world therefore he can't be reproduced in lab or reproduced in a beaker or test tube.
Scientists are steadfast in attempting to review all angles of a naturalistic proposition, but "natural" is where it stops. Certainly cosmologists and physicists will entertain the notion of metaphysical conditions, but they conform that seemingly transcendent condition to their naturalistic perspective. In essence, what you assume to be true will sometimes be proven to be true if all you seek is what you want to be true.
Ask the scientific community to proactively follow the lead of a theist to test the scriptural claims of the transcendent God and laughter ensues; yet, the scientific community demands that the scientific method be followed and naturalistic evidence for a transcendent God be provided.
I don't personally know how to overcome that.