To inculcate means “to implant by repeated statement or admonition; teach persistently and earnestly” or “to cause or influence (someone) to accept an idea or feeling”.
From the Online Etymology Dictionary, it comes from Latin “in- ‘in’ + calcare ‘to tread, press in,’ from calx ‘heel.’”
Makes perfect sense. The way some teachers are, it really feels like they’re trying to dig their heel into your brain.