I have my answer. Actually I have several answers, but it usually comes back to an externality-based argument.
One that I don't focus on too much is spin-off technologies (although these are special types of externalities themselves). Yet for some reason spin-offs can seem like the definitive justification for public investment in science by non-economist public science enthusiasts.
I think this is unfortunate and someday I'd like to articulate for a general audience why spin-off technology is not the strongest justification for public science available.