How do you explain homeschooling to sceptical in-laws?

Show, do not argue. Invite them to a co-op morning, a project presentation, a museum visit. What they see outperforms any argument.

Share results. When our son's reading was two years ahead of age expectation, we showed grandparents the assessment result.

Lower the temperature. Focus on specific evidence of the children's wellbeing. A thriving grandchild is harder to argue against than a theory.

Time. After three years our in-laws stopped arguing and started noticing. The evidence accumulated around them.