"because it wants to tax some of it which seemed incorrect"

Yes, your taxpayer will be paying taxes on the earnings amount, which will be seen as a pro rata percentage.

Invest $7k into a Trad IRA account as nondeductible on the tax form, and let's assume it grows at 10% APR ($350) and 6 months later, invest another $7k and on that same date, convert all of this to Roth.

Assume there are no other funds in accounts that fall in the same category as Trad IRA.

The math is: $350 earnings (never taxed)/$14,350 basis (post-tax) = 2.44% taxable. If there are other funds in Trad IRA or similar account type(s), then the math on any conversion changes accordingly.

A "backdoor" is just a conversion done on Basis and done so quickly it avoids having earnings. At least, that's the plan.