Carbon neutral jet fuel exists (synthetic fuels from electrolysis, and/or biofuels), and could be scaled up. The issue is not “can we do this”, it’s “can we justify doing this economically”.
Biofuels seem mostly like a crock, honestly -- the ones we can produce now compete with food for arable land and would do so more aggressively at scale, and the ones that wouldn't do that (algal fuels, maybe cellulosic fuels like switchgrass) still require fundamental R&D to make the economics work. And again: even if they did work, this is a solution where you're burning fuels and emitting carbon, and then remedying by capturing again, this time with plants. So again: it's carbon capture.