Public School: A qualified teacher with proven subject matter knowledge who is accountable, a curated curriculum designed by teaching and subject matter experts, as well as a meaningful diploma which actually lets colleges/employers understand roughly what you were taught and how you performed

Homeschooling: some random mom, with some random level, including potentially none at all, of qualifications and subject matter knowledge, and little to no curriculum supervision, and resulting in zero credible or meaningful certification

You do the math