The ad hominem fallacy is perhaps the most well known, and frequently committed fallacy, simply because it most appeals to human nature. We've all seen it committed, and have more than likely committed it, and been called out for it, ourselves. It is commonly misunderstood, however, to the extent where it is often misidentified (i.e. someone has been accused of making it, but hasn't), and almost as often missed.
The term "ad hominem" is Latin, literally translating to "to the man". This is because the fallacy is an irrelevant focus on "the man" making an argument, or holding a belief, rather than the quality of the argument or belief. Specifically, it is an irrelevant appeal to something about one's opponent.
This is typically divided into 5 sub-categories: Abusive, circumstantial, bias, tu quoque, and poisoning the well.
An abusive ad hominem is a call for an argument or belief to be rejected based on some apparently negative trait, such as one's appearance, personal taste, intelligence levels, or even some character trait. With the possible exception of a character trait (e.g. if someone is known to be a compulsive liar, it is entirely relevant to doubt their testimony on this basis), none of these things are relevant to an argument they may make, or a belief they may hold.
A circumstantial ad hominem is a call for an argument or belief to be rejected based on irrelevant circumstances of the one being attacked. In effect, "that's what we'd expect you to say", which may even be true, but not to the extent of invalidating what has been said. For example, we would expect a high school graduate to say the Earth is round, but this is irrelevant to whether or not the Earth is round. In a similar vein is the bias ad hominem, which suggests the one being attacked has something to gain if their arguments or beliefs are taken seriously. This differs only slightly from the circumstantial ad hominem. Ultimately, this is a fallacy because one's personal circumstances, and even motives, do not affect the validity of their beliefs or arguments, as beliefs or arguments should stand or fall on their merits, not the one making or holding them. It should be noted, these things very rarely work the other way around. When someone speaks who should be biased the other way, or who is in the opposite circumstance (such as black people speaking out against reparations, or rejecting the belief in white privilege), this simply results in the abusive ad hominem being applied instead.
The Tu Quoque ad hominem is also known as the appeal to hypocrisy fallacy, with "Tu Quoque" literally meaning "you too", or "you also". As one might expect, it is the "Uno reverse card" logic we see in all kinds of debates, both religious and political. "How can you oppose this, while you support that?" The simple fact is, if the charge of hypocrisy is correct, it doesn't erase the original charge, it just means both sides have a problem to address.
Finally, there is the poisoning the well ad hominem. Named after an old European conspiracy theory that the Jews would literally poison wells, a lie that would result in much anti-Semitism across Europe, the poisoning the well ad hominem is a pre-emptive ad hominem fallacy, casting some kind of doubt upon one's opponent before they even have the chance to speak. "Only a racist can support this belief", "only a bigot can oppose this policy", "this person is in this group, so naturally they're going to believe this way".
All of these types of arguments fall short because they take the discussion away from the topic at hand, and instead focus on one's opponents. Ultimately, a belief or argument must stand or fall on its own merits, because the truth remains the same regardless of whose mouth it comes out of. Of course, there are exceptions. "I am 100 years old" is a true statement when a 100 year old says it, but not when anyone else says it.
One of the most common examples of the ad hominem fallacy in today's world is "no uterus, no opinion". This slogan is applied when men speak out against abortion, ultimately summarising the circumstantial ad hominem argument that men, as we are unable to get pregnant under any circumstances, should not be allowed to speak on the morality of when a pregnancy should be "terminated". The main problem with this argument is that it can only be applied to men. If you were to read an anonymous article arguing against abortion without any reference to the author, could you reasonably say "no uterus, no opinion"? Of course not, because you only have a 50% chance that the author doesn't have a uterus. On top of this, there is a possibility that a pro-life man may be simply regurgitating what he has heard from women. I know I, personally, have done this many times in my opposition to abortion.
It is important to note that insults, while childish, are not necessarily ad hominems. To qualify as an ad hominem, the attack must be linked to the argument being made, whereas if an argument is made and followed by an insult, that's just the debater being a jerk. The argument can even be broken down and rephrased to omit the insult. Furthermore, an ad hominem does not necessarily have to be an insult, as we have seen above. There is nothing wrong with being a man, just as there is nothing wrong with being a woman, it's just that, sometimes, weak minded people see gender as something that is relevant to a debate.
If you have understood this article thoroughly, you may have already noticed the (quite intentional, for instructive purposes) poisoning the well, abusive ad hominem I made just now. I said "weak minded people see gender as something that is relevant to a debate". This would be an ad hominem, because if anyone wanted to oppose my belief that gender is not relevant to a debate, I would have already impugned them as "weak minded". While this is something I genuinely believe, the strength of someone's mind is, ultimately, not relevant to whether or not gender is relevant to a debate. Thus, if I was to debate the topic "is gender relevant to a debate", I would have committed the poisoning the well ad hominem fallacy by pre-emptively impugning the character (i.e. abusive ad hominem, the attack is based on some negative trait) of any opponent I might face.
The ad hominem fallacy can fairly easily be exposed, as it is a simple matter of removing the opponent from the debate, figuratively speaking. As previously mentioned in the abortion example, you can only apply the argument "no uterus, no opinion" to men, because women do have uteri. If you can switch out a debater and the argument immediately becomes invalid, it is always invalid.