Critic: An art historian argues that because fifteenth-century European paintings were generally more planimetric (that is, two-dimensional with no attempt at suggesting depth) than were sixteenth-century paintings, fifteenth-century painters had a greater mastery of painting than did sixteenth-century painters. However, this conclusion is wrong. Fifteenth-century European painters did not have a greater mastery of painting, for the degree to which a painting is planimetric is irrelevant to the painter's mastery.
The argument is flawed in that it
rejects a position merely because the proponent of the position has other objectionable views
The critic never mentions any “other objectionable views.” She just objects to the view that fifteenth-century painters had a greater mastery of painting. Instead of (A), the critic rejects a position merely because she has weakened the historian’s support for that position.
illicitly relies on two different meanings of the term "mastery"
This is the cookie-cutter flaw of equivocation, where the author uses the same term in different ways without acknowledging the shift in meaning. The critic doesn’t make this mistake. She uses the word “mastery” consistently throughout her argument.
takes a necessary condition for an argument's being inadequate to be a sufficient condition for an argument's being inadequate
This is the cookie-cutter flaw of confusing necessary and sufficient conditions. The critic doesn't make this mistake. She doesn’t rely on conditional logic. Instead, she rejects the historian’s conclusion just because she weakened the historian’s support.
bases its conclusion on two claims that contradict each other
The critic contradicts the historian’s claim, but she doesn’t have an internal contradiction within her own argument. That is, her conclusion isn’t based on two premises that contradict each other.
rejects a position on the grounds that an inadequate argument has been made for it
The critic rejects the historian’s conclusion on the grounds that her support is weak. But it’s possible that fifteenth-century European painters did have a greater mastery of paining, even though a painting being planimetric doesn’t reflect the painter’s mastery.