When there's inconsistency, things are not the same. An example of inconsistency in parenting might be when parents give different allowances to kids who are the same age.
There's a lot of inconsistency in the world. Some restaurants will serve delicious food most of the time, but not all the time. Teachers in different classes will have different rules for what is expected. Another type of inconsistency is between ideas or propositions. For example, if you want to lose weight but cannot stop eating donuts, there is a major inconsistency between those two ideas. Anywhere you find things that are changing or varying, there is inconsistency.