  Stars in galaxies form from the cold rotationally supported gaseous disks
that settle at the center of dark matter halos. In the simplest models, such
angular momentum is acquired early on at the time of collapse of the halo and
preserved thereafter, implying a well-aligned spin for the stellar and gaseous
component. Observations however have shown the presence of gaseous disks in
counterrotation with the stars. We use the Illustris numerical simulations to
study the origin of such counterrotation in low mass galaxies ($M_\star = 2
\times 10^9$ - $5 \times 10^{10}\; \rm M_\odot$), a sample where mergers have
not played a significant role. Only ${\sim}1\%$ of our sample shows a
counterrotating gaseous disk at $z=0$. These counterrotating disks arise in
galaxies that have had a significant episode of gas removal followed by the
acquisition of new gas with misaligned angular momentum. In our simulations, we
identify two main channels responsible for the gas loss: a strong feedback
burst and gas stripping during a fly-by passage through a more massive group
environment. Once settled, counterrotation can be long-lived with several
galaxies in our sample displaying misaligned components consistently for more
than $2$ Gyr. As a result, no major correlation with the present day
environment or structural properties might remain, except for a slight
preference for early type morphologies and a lower than average gas content at
a given stellar mass.
