Currently, single parent families are one of the fastest growing types of families there is. Separated, widowed, divorced, single by choice, de facto, and same sex couples living apart can all fit into the category of a single parent family.
Common interests and experiences unite sole parents and bring together individuals who may not ever have normally met. The assumption that single parent groups are just an excuse for sole parents to meet and form new relationships with others is inaccurate.
It can be hard to redevelop skills in communicating with others as a single person, rather than being part of a couple. After separation, loneliness can be a common theme amongst sole parents.
For many, this may be an emotion they have become unfamiliar with and are at a loss in knowing how to deal with it. Some interpret loneliness as depression, or feeling down and dissatisfied with their lives, when in fact it can be just one symptom of needing other adults company.
Parents need other adults for company, conversation and just companionship. No matter how independent you are, avoid seeing yourself as having different needs to the rest of the human population. It is unlikely you would consider isolating your children from others of their age group so why extend this expectation to yourself? Finding a connection with people who are going through similar experiences can be invaluable. Joining a single parent group means that you can avoid awkward explanations and small talk in having "Single parent meeting groups" explain your circumstances.
By definition, you have met the criteria for inclusion and are seeking the same opportunities as everyone else there.