Jacksonville (and most of Florida) is extremely low lying with a high water table, so sub-surface construction (basements) and subways are basically impossible.

Structurally, it's a low density, car-based city so light rail (as opposed to busses) requires a lot of up front investment without the land use to justify it. At this point, like many US cities, adding effective transit is a chicken and egg problem with land use.

There are a couple reasons (not the least of which is political will but that's a separate discussion). Jacksonville sits on a coastal plain and is almost entirely fine sand. You simply can't build a subway in that without astronomical cost. As for rail I'm pretty sure Jacksonville already has elevated rail in some places but ground rail would be difficult for the same reasons.

It's the 2nd least dense large city in America. It has a population of San Francisco but across like 15x more land.

Austin is the 12th most populous city so it's possible they're just wrong but probably not.