Born is a rare English Deponent verb -- there may be more of them, but I can't think of any others offhand. A deponent verb is a verb that is passive in form (like be born) but not passive in meaning. This is an irregularity in a sense, because the usual forms don't have the usual meanings, but in inflected languages they are often very useful.
Latin had flocks of deponent verbs, but then in Latin it was easy to tell a Passive verb from an Active verb, because they had totally different endings. And at that, Latin was simpler than Greek or Sanskrit, which had separate Active, Passive, and Middle voice paradigms, and several different types of deponent verbs to go with them.
While it is a fact about humans that we are all borne by our mothers (which is a true passive), the universality of the event means that one's mother need not be mentioned every time one refers to one's birth year, for instance. The agent subject can be understood, since it contributes no new information. Consequently the overtly passive constructions of born in
- He was born in 1858 and died in 1932.
- Anderson, born in 1858, died in 1932.
- Millicent Anderson, born and died the same year
are semantically and syntactically parallel with die, which is a punctual (happens at a point of time) inchoative (change of state) predicate, exactly like (be) born, even though die is active in form and requires no auxiliary be. Born and die even have parallel irregular nominalizations birth and death.
Executive summary: Pay no attention to official parts of speech. Look at the grammar instead.