There are many good reasons families could have for not homeschooling, but I do not think socialization is one of them. Yet, it is a top reason for parents not to homeschool, but it is really a myth. And I will tell you why.
One big reason is our modern public and some private schools are not great models for socialization. These are schools that segregate children in groups by age and geographic location with limited interaction with more than one adult at a time. Life does not work that way, nor does it prepare them for the workforce or being apart of the community. Children have more time to learn social skills from their peers than from their parents, another words - they become peer dependent. Who do you want you child to learn social skills from yourself or another 8 year old? Who do you think has more wisdom to pass along?
A functional family unit is a great model for children, after all they will probably have a family of their own one day. I always say, the hardest people to get along with is your own family, and I never have had one person disagreed on that point. Just think of how different each personality is in your family. Homeschooling is great at exposing issues, especially of the heart, that lie underneath the surface. Plus, homeschooling gives you the time and motivation to work out those issues.
There are those few homeschoolers that completely cut themselves off from the outside world, and yes, those kids probably will turn out weird. However, I also remember quite a number of weird people that I went to school with and none of them were ever homeschooled. What I am saying is that the social misfits of society will be society misfits whether they are homeschooled or not. Actually, public/private school would magnify the "different" child's weird behavior because of high level of bulling and teasing.
As far as homeschooling social activities, there is more out there than you could possibly do. Homeschooling also leaves more time for social activities because there is no homework and during the elementary years, most children are done by lunch time. Then it is off to art class or music lessons, maybe sports or dance - or just playing at the park with a bunch of friends. Where ever you live, I am sure there is a homeschooling support group that plans events, park days and field trips. Homeschoolers tend to be more involved in their community, like 4H clubs, library events and outreaches through your church. Actually, there are so many opportunities, that homeschooling moms can burn themselves out by going to too many activities.
One great homeschooling activity is belonging to a homeschooling co-op. This is a group of homeschooling families that met at least once a week for classes in a "school" type setting, sharing the teaching responsibilities. At a co-op your child will learn how to work in a group outside of the family; take instruction from other adults; and build relationships of their choosing (not because they just happen to have lunch the same period). It is also great socialization for the moms too! Plus, it is a good chance for children to learn some of the hard lessons in life - like being teased, but learn them on a more manageable scale. By middle school and high school, most homeschoolers start taking some of their classes outside the home by paid teachers in homeschooling organizations or county college. This actually gives them a similar experience as they will receive in college - classes once or twice a week and doing their assignments between on their own.
In all of these opportunities for homeschoolers, they will be able to interact with a wide age span. A 5 year old and a 7 year old can be friends. A co-op class may have an age span of 7 to 10 in one class. A homeschooling field trip may have kids from preschool through high school, like the piano factory tour our family went on. During these times, your family will build relationships in the homeschooling community that will last year to year.
When people ask me, "What about socialization?" I answer, "Yes, that is one of the reasons why we homeschool."
Here is a link to Homeschool Legal Defense Association's website about socialization if you want to know more. There have been studies on the subject by universities as well.
Just on a personal note, I have nothing against public or private schools. My education took place at both. I also feel that free public education is essential to a nations peace and prosperity, as well as the personal enjoyment in the life of each citizen. Also, I believe being a teacher is a very important job and deserves an elevated level of status in our society.