Well, when Kirk brought up Amanda, he was intentionally trying to provoke
Spock. Kirk used the most abrasive language that he could. So naturally Spock's emotional outburst would be a result of that.
But when Spock mentioned Kirk's father in the earlier scene, Spock wasn't trying to make Kirk mad or anything like that. Spock didn't say anything that Kirk didn't already know. Spock was being as 'diplomatic' as possible - he wasn't bashing or insulting Kirk, just trying to make a point.