It's an entitlement program because what you're entitled to it independently of what you put in. There's no isolation. You don't suddenly get cut off when "your" contribution has been exhausted. You keep drawing from the pool, indefinitely, and in fact this is the common case because official estimates of what people need for retirement (both cost per year and longevity) consistently lag behind reality. The pool "just happens" to be replenished mostly from still-working folks' contributions, but it's still a pool and not individual accounts.

Before anyone else "well actually"s me, as a retiree myself I'm well aware that there is some relationship between what you put in and what you get out. That doesn't change the system's essential nature. It's more of an anti-abuse and anti-depletion measure, similar to raising the retirement age or adding means tests. There's still a big common pool in the middle, and people can still keep drawing from that pool even if they live well beyond the point where their net contribution is negative.