Humanity was socializing long before public schools existed, and by no means does the present public school system have a monopoly on teaching social skills.
Statistically, home schools produce outstanding educational outcomes compared to public schools on standardized tests, so public education proponents insist that they compensate for this by providing better "socialization". This claim is conveniently difficult to refute with hard data since "socialization" is harder to quantify, but it doesn't prove public schooling produces better socialization outcomes.
To the contrary, homeschooling is so effective at education because it's taylored to a particular student's developmental level in each area, including socialization. Home educators have tremendous schedule flexibility, and in many areas, large co-op resources, presenting endless opportunities for friendship, teamwork, conflict, community service, and time to develop their own interests (programming? theater?) with other like minded students. For instance, while day-school students are stuck in a room not interacting with one another, a nine year old home schooled student may attend day rehearsals for a play at the local university, volunteer at a local food bank, or build robots with their FRC team, all before playing little league baseball after the day school students become available. These opportunities don't just lock students into same age groups all day for 10 years, but allow time for them to participate in the real world community outside with a broad range of both peers and adults.
The diversity of opportunities for homeschool students often results in a student whose social experience and civic responsibility is as outstanding as their standardized test scores. You can absolutely homeschool social skills.