Thank you for choosing Ask an Expert for help with your cabbage. I do suspect bacterial soft rot. This disease attacks primarily under cooler temperatures combined with extended periods of moisture, whether from rain or from watering. It can be spread by splashing, hands, or clothing. 

There’s nothing we can do about the rain, but reducing overhead watering, as much as possible, can help–especially as heads are forming. Early morning watering is preferable, because it has all day to dry off.

Make sure plants are spaced to provide good air circulation to allow for drying and to decrease humidity. Damage to the plants while weeding or cultivating can open up places for the disease to enter.

Though this disease can be spread by insects damaging the plant leaves, I'm not sure this insect is the culprit. Many beneficial insects appear to "clean up" when plants are damaged.

Have a good gardening year,