If a fedora-tipping atheist goes up to a Christian who says that homosexuality is a sin, and says "But I bet you eat shellfish, huh? Isn't that an abomination too?", that is a bad faith argument because the neckbeard does not themselves believe in the moral authority of the Bible. It's an argument, perhaps, for the hypocrisy of someone who follows one line from Leviticus but not another, but it is not an argument about the morality or otherwise of homosexuality - it's just a personal attack on the other person, achieved by pretending that the Bible has moral authority (and that if you obey some of it you should obey all of it) from someone who actually believes that you shouldn't obey any of it.
However if a Christian who indeed does not eat shellfish because Leviticus said not to attacks another Christian who does with exactly the same argument that is not a bad faith argument, because that first person agrees with the second that the Bible is a source of moral instruction, and that the second is interpreting it incorrectly and doing something morally wrong (eating shellfish) as a result.
As I see it a bad faith argument is misrepresenting your own beliefs to "win" an argument with someone ("concern trolling"). However, as the above example shows, by arguing in such a way the best you can achieve is attacking a person's character in terms of how their beliefs or behaviour match their own ideology, but they can't address the correctness or otherwise of the ideology itself.
In a legal sense, "bad faith" means misrepresenting your intentions with regard to another party to gain an advantage over them. For example, if Company A announced it was going to acquire a rival Company B, and asked to go over Company B's internal documentation to do "due diligence", but never completed the takeover, and in fact never intended to buy it and just wanted to spy on it, that's an act of Bad Faith and Company B may have grounds to sue.
