We investigate emulsion droplet formation in coflowing liquid streams based on a computational fluid dynamics simulation using the volume-of-fluid method to track the interface motion with a focus on the dynamics of the dripping and jetting regimes. The simulations reproduce dripping, widening jetting and narrowing jetting simultaneously in a coflowing microchannel in agreement with the experimental observations in this work. The result indicates that the dripping regime, rather than the jetting regime, is a favorable way to producing monodisperse emulsions. We find that, in dripping and widening jetting regimes, the breakup of a drop is induced by higher pressure in the neck which squeezes liquid into the lower-pressure region in subsequent and primary droplets, while the breakup in the narrowing jetting regime is due to slow velocity at the back end of the trough with respect to the leading end of the trough. In addition, the capillary number of the outer fluid and the Weber number of the inner fluid not only determine the drop diameter and generation rate but also the regime of emulsification.