It's stating a fact if it is true, not an insult. However it is different if you are calling someone fat because while that is also stating a fact it is a hurtful thing to say and being fat isn't immoral like how lying is. Also it is obvious if someone is fat where as if someone is a liar it isn't so there is no point in pointing out that someone is fat but there is if someone is lying.

If it's simply a mentioning of a fact then it's not. It depends on the intention of the one calling out a liar. However, in the large majority of cases, there's an intention behind words.

If it's meant to hurt the liar, then it's an insult. If there's any kind of ill will aimed towards the person, then it's an insult. If, on the other hand, it's meant as a helpful reminder, then I don't see it as an insult. If am telling you that you are lying in order help you snap out of some bad mental habit, then it's a kind thing, not an insult.

The key here is the intention. If you call someone out of compassion for the person, it's not an insult. Otherwise, not so.

Generally speaking, no- but it can be, depending on the circumstances.

For example, if you take affront to a little white lie on an issue that is just between you and the liar, and proceed to publically call them a liar in front of friends, family, etc- that is certainly insulting and inappropriate.

No not necessarily, you can be just calling it the way it is.

However it can be said in an insulting manor even when stating fact.

So in all actuality this can go either way and is more of a gray area (non-specific) and should have been put as a perspectives debate.

If a person is caught in lying, he should be address of his mistake.