In the strictest sense, an entitlement program is one that guarantees benefits to anyone who meets certain eligibility requirements. Social Security and Medicare are prime examples – if you meet the age and contribution requirements, you are entitled to the benefits.
Public education in the United States isn't structured exactly like that. While most children have a right to a free public education, it's not always guaranteed in the same way as Social Security. The specific details vary by state and locality; funding mechanisms differ, and there might be limited exceptions based on things like residency or special educational needs. There's also no guaranteed level of quality.
Therefore, while public education is a fundamental right in the U.S. (as implied by Supreme Court rulings and widely accepted), it's not an entitlement in the same vein as Social Security or Medicare. It's more accurate to say it's a right *funded* through an entitlement system (taxes), but the education itself isn't unconditionally guaranteed in the same way. The term "entitlement" is often used more loosely in public discourse, leading to the ambiguity.