And you're just flat out incorrect
https://www.nysenate.gov/legislation/laws/PEN/35.20
- A person in possession or control of, or licensed or privileged to
be in, a dwelling or an occupied building, who reasonably believes that
another person is committing or attempting to commit a burglary of such
dwelling or building, may use deadly physical force upon such other
person when he or she reasonably believes such to be necessary to
prevent or terminate the commission or attempted commission of such
burglary.