No, that's also a misunderstanding of ad hominem fallacy, since I dismissed it by directly addressing your claims validity. Even by your definition, this conversation is propaganda.
But here are some additional definitions:
Propaganda: ideas, facts, or allegations spread deliberately to further one's cause or to damage an opposing cause
Propaganda: The systematic dissemination of information, esp. in a biased or misleading way, in order to promote a particular cause or point of view, often a political agenda.