I understand quite well how you'd like to frame the topic, yes. To use the terminology of the page you linked to: education quite clearly qualifies as both rival (since it has non-zero per-student costs) and excludable (since each student participates in education individually), which makes it not a public good by the definition you linked to.
I never stated a belief about whether or not education is a public good. The person I responded to stated that law enforcement is a public good but not education. I wanted to know why he/she thought this. I don't see how one can be considered a public good and not the other.
While law enforcement has some potentially excludable components, for the most part it seems non-excludable: stopping crimes and criminals protects everyone. Exclusion mostly seems possible geographically, and we already effectively do that at the borders of states and countries. On top of that, unlike education, law enforcement does not have a blindingly obvious solution for how to run it privately. (While I understand that solutions exist for how to "privatize" law enforcement, any attempt to privatize the use of force has huge difficulties and dangerous pitfalls.)
