The sentence that presents the strongest and most reasonable counterclaim to the claim that "it is more enjoyable to eat ice cream in a cone than in a cup" is:
"When ice cream melts, it can dissolve the bottom of a cone and leak through."
This counterclaim addresses a practical downside of eating ice cream in a cone, highlighting a potential issue that could detract from the enjoyment of the experience. It presents a specific scenario that could negatively affect the enjoyment factor, making it a compelling argument against the original claim.