The complaint I have heard the most often any time myself or others in my team have pushed forward with a new idea is "but that's not the way we do things". The appeal, when divorced from the obvious truth of such a statement, is that what we currently do works. So what advantage would we get from changing?
This is a question we always need to ask ourselves, because being agile is not change for the sake of change. There is usually an identification of a deficiency, inefficiency, or bottleneck that the suggestion tries to address.
We have a deficiency now in that the database changes are wholly separate to the code changes they align with. When we deploy, we have to coordinate with the DBAs to make sure they run their scripts at the right time. This is fine when they are available, but a problem when they aren't.
But even if they were always available, it's a coordination problem that can be easily solved by scripting. As it stands, anyone can deploy to Test whenever there is a need to do so. And there's currently no obvious way beyond the developers knowing what changes are going in as to whether the DBA is required.
Evidently this is a fairly common problem because there are multiple products that solve it by introducing DB versioning. The main resistance is getting the DBAs themselves on board.
They are correct in that it's a cultural change, moving away from a system that works. But it's a necessary change because the system as it works has obvious (and sometimes painfully pressing) limitations. We want this change because we can and need to do better than what we have.
It's good to have a reminder that development is largely people, so we should be mindful of how people can react to being asked to change.