Determinism as a philosophical position is hard to counter.
If we didn't have an overwhelming internal sense of making choices, I don't think anyone would argue against it.
So much of our life is conformed by habit, conditioning, state of health etc, that even I, taking a non Determinist position, accept that 90% of what we do is not in our conscious control.
Different Point.
I think there is a problem for Determinism when we shape the world in a way which isn't Utilitarian.
So, houses might be explained by Determinism, and offices etc, but the existence of the Taj Mahal, a monument to human grief, is harder to explain.
In fact, the whole of art is a problem for Determinism, isn't it?
If the mind does not control the body, then how could people make things that can only be understood by referring them to that mind?
I'll put it another way.
Why are there things in the world which indicate the existence of a human mind if that mind can have no influence in making them?