Special pleading

Special pleading (or claiming that something is an overwhelming exception) is a logical fallacy asking for an exception to a rule to be applied to a specific case, without proper justification of why that case deserves an exemption. Usually this is because in order for an argument to work, a proponent needs to provide some way to get out of a logical inconsistency — in a lot of cases, this will be the fact that the argument contradicts past arguments or actions. Therefore, proponents introduce a "special case" or an exception to their rules. While this is acceptable in genuine special cases, it becomes a fallacy when a person doesn't adequately justify why the case is special.

The fallacy is a conditional fallacy, because special cases do exist; in other cases, the fallacy is circular ad hoc.

Structure
A person accepts a certain set of criteria for judging something, and applies this in a way appearing consistent and completely exhaustive. Said person finds themselves somehow restricted by their own criteria, and declares their own case "special" without any real justification and excludes themselves from their own principles to make their case.

This is a fallacy because they are claiming that they are exempt from certain principles or standards, yet they provide no good reason for their exemption. A real exception would either be easily justifiable or apparent in the conditions they make in the first place, such as "these standards apply to x, y, and z because of a, b and c" and people can then agree with this and the reasoning. Simply demanding that an exception be made is not enough.

The fallacy is circular in structure. The only reason that example X is not disproven by evidence Y is that example X is disproven by evidence Y.

Explanation
The key to this being a fallacy is that there is no adequate reason for treating the situation differently. Since a different situation is, by definition, different, there is always some distinction to be made; the issue is whether this difference is sufficient. Obviously, the person making the argument thinks that it is sufficient, and stating that it is not will simply be dismissed as not recognizing the fact that this situation is totally different.

Examples

 * In the Thomistic cosmological argument for the existence of God, everything requires a cause. However, proponents of the argument then create a special case where God doesn't need a cause, but they can't say why in any particularly rigorous fashion. Two additional points are worth adding:
 * One response to this argument, beyond pointing out the fallacy, would be to point out that nature itself could have existed eternally in some form just as they say God had existed eternally before creating nature. One modern philosopher who has applied this argument is Carl Sagan, though he wasn't the first to do so.
 * That being said, such a special pleading when discussing a "First Cause" may have some degree of merit; as any computer scientist will tell you, the root of a nested hierarchy may need to be handled as a special case anyway, although said computer scientist can probably also add that there are plenty of that have multiple roots.
 * The seemingly hypocritical nature of some politicians regarding drug use or sexual misdemeanors. Specifically, the typical position is that alcohol and tobacco are OK, but other less harmful drugs are not, regardless of any scientific evidence about the relative harm of each drug. Or pundits who insist drug users should be executed, but turn out to be drug addicts themselves and pretend it's somehow "different" for them.
 * Biblical morality takes massive amounts of special pleading from Biblical literalists who insist that morality can only come from the Bible. They are very happy to follow some rules (shunning gay men, which being in spite of equivocation in and  and implied special pleading in, , and ) but not others (selling their daughters into slavery, stoning disobedient children, eschewing shellfish) — even though the Bible, which they claim can be the only source of their moral decision making, is quite silent on what parts of it you can happily ignore.
 * Some conspiracy theorists believe that all conspiracies are bogus except their favorite one. This does not appear to be special pleading superficially, but if you investigate the logic behind the examined conspiracy theories, you will find it inconsistent to believe in only one of them.
 * In the Virginia personhood law, which grants the zygote the rights of an adult, item 7 states that "nothing in this section shall be interpreted as affecting lawful assisted conception." In in vitro fertilization, though, several oocytes are removed from a woman's ovary, bathed in semen and fertilized, let to develop into blastocysts, then the ones that look "healthiest" are selected to implant in the woman's womb. The several blastocysts left over are then treated as medical waste.
 * With regards to laws protecting LGBT workers from discrimination, it is argued by the far right (such as evangelicals and other conservative Christians) that because an employer owns a business, they should have full autonomy with regards to hiring and firing. There are plenty of demographics of people that employers cannot legally discriminate against, yet this point usually remains unaddressed — probably because if the same logic were applied toward a race or a sex, the arguer would be committing political suicide. It is sometimes then counter-argued that this exception is logically permissible, because "homosexuality is a choice".

In law
Special pleading is an obsolete term in English law, defined by the Oxford English Dictionary as:
 * 1) A pleading drawn with particular reference to the circumstances of a case, as opposed to general pleading (1684).
 * 2) The putting forward of special pleadings; the art or science of drawing pleadings (1768).

In practice, that often meant arguing for a case to be dismissed, regardless of its merits, because of formal defects in the other side's documents. If you had a winning case, you might not bother; but if you wanted to get away with murder, you surely would.