Public school is not a guarantee that you will have friends.
But homeschooling is a near-certain statistical guarantee that you won't.
Before you drag me down on the semantics of that one, allow me to clarify the meaning of friend. To me, a friend is an individual who I hold trust in, who I can speak to meaningfully, and who I respect. These attributes obviously must hold true reciprocally. Homeschoolers do not tend to have figures in their lives who meet these criteria, even if they do have acquaintances who their parents call "friends" to make themselves feel better.
I'll never forget my mom talking with one of her friends and referring to a kid my brother barely knows as "one of his best friends." Have you ever had a moment when you don't know whether to laugh or cry?