"Could we possibly praise the Mona Lisa without praising Leonardo DaVinci?"
That is a truly beautiful analogy.
It truly captures the meaning of the veneration of the saints, especially of the Theotokos.
The reason is simply that absolutely everybody knows that every artist and engineer relies to an incredible degree on certain genes that he's inherited to make it possible for him to do his work. Without those genes no amount of training will turn you into a painter, architect, design engineer, etc.
Mary was selected directly by God for her mission. Politically she had the correct putative ancestry (being a descendant in the traditional Royal House), but as far as the genes are concerned, unless we want to get into the "what does the term 'fruit of thy loins' really mean in a scientific sense" discussion, it's more nearly correct to discuss her only in terms of "grace". Leonardo certainly was not operating under "grace" from anyone unless it was Rene d'Anjou who fought a war with Padua to capture him and take him to France where the King had built a university just for him. Rene had already served his time as God's annointed on Earth (he was a Cardinal too) when he became the political sponsor of Jeanne d'Arc. The King of France, of course, betrayed Jeanne to the Burgundians and they to the English.
I'm not sure Mary would be too happy about having her name get linked up in a thread of thought that includes burning Jeanne d'Arc at the stake!
Even folks not terribly into Mariology might find that connection a bit rough. So, find another dichotomy to use as an analogy for your argument.