Something inexcusable doesn't have an excuse, justification, or reason. Inexcusable things are horribile and unforgivable.
Getting sick is an excuse for missing school. When an action is inexcusable, there is no excuse for it. Inexcusable actions and words don't have a justification. Also, this word is used for things that are just plain awful. Most people would say crimes like murder are inexcusable. If a good friend lied to you, you might consider that inexcusable. This is a harsh word for things that we can't forgive or condone.