The fallacy of proving too much occurs when someone puts forward an argument that would apply not only to the intended conclusion, but also to a much broader range of conclusions, including some that any reasonable person (or all participants in the conversation, at least) would regard as absurd.
Here is an example:

Son: "Mom, I shouldn't have to go to school today."
Mom: "Well, you need to learn and not fall behind the rest of the class. With that in mind, why do you think you still shouldn't have to go?"
Son: "Because I'm tired, and people shouldn't have to go somewhere when they are tired, even if there is a reason to go."
Mom: "That would mean that whenever I'm tired, I shouldn't have to go to the grocery store, even if we need food; I shouldn't have to go to the doctor, even if one of you kids is sick and needs to be taken in; I shouldn't have to go to work, even if we need money to pay the rent; and so on, for many other things."
Son: "Well, I hadn't thought of all that."
The son initially "proved too much" in that his major premise, if accepted, would imply all the other conclusions pointed out by his mom.