Let’s look at the definition of correlation. It states that casuality is ONE of the ways a correlation is made.
Now your statement says that “correlation does not imply causation”. Actually, I beg to differ. Correlation DOES IMPLY causation.
Is correlation PROOF of causation? No. But it does IMPLY, which has a lesser burden of proof.
Personally I don’t believe that homeownership in and of itself is the CAUSE of improved childhood academic success. However, I cannot say that it ISN’T either.