Reasoning by Criteria

The most difficult kind of reasoning I found to understand was reasoning by criteria.  I am confused as to what exactly distinguishes this kind of reasoning with any other kinds of argument since every argument has some kind of criteria or topic that must be met in order to make sense.
According to changingminds.org reasoning by criteria is most helpful when you are trying to argue against something. Once you establish a criteria in an argument it is easy to refute and find the flaws in the premise. Also when you establish the criteria you can judge what will be the best choice to make based on the standard given. "The easier criteria are to accept as reasonable, the less likely it will be that people will question them. Using common values helps this."
For example, having gone to a Catholic high school, I have heard many arguments about whether or not abortion should be legal in this country and the rest of the world. A good way to argue against abortion would be to state common values that both religious and non-religious people could agree on, such as abortion can be dangerous for the mother, if the fetus has a beating heart it is a living being, it is the mother's sole responsibility to do what is right for her unborn child. People who are for the legality of abortion can argue that it is not murder since the fetus is not necessarily a person because it cannot live on its own, there are many situations where it would be more harmful for the mother if she kept the child such as deformities and other health problems.
But the important part of reasoning by criteria is establishing the rules and standards by which the argument can progress to. The person arguing can make their argument stronger by establishing the boundaries that they can follow in order to win the majority of audience.