Inexcusable is for behaviour that is too bad to excuse. You have run out of reasons. Being late once can be excused; lying to cover it, or hurting someone on purpose, can be inexcusable. It is a strong, judging word, used by adults, news writers, and anyone who wants to say “this is not all right, and please do not try to explain it away.” It is about what someone did, not about a small slip in a sum. Though actually, people stretch it when they are angry — a missed message can be called inexcusable in a fight even when, in a calmer hour, it would only be rude or careless. The word is formal, but the feeling behind it is plain: the line has been crossed.