But that's an ad hominem argument and you stated you believe such arguments are valid. So why isn't this one valid, and what are the criteria for valid ad hominem arguments, in your opinion? Why, for example, is your accusation that I was lying valid? That argument was tantamount to, "you're just saying that because you are a liar". Why is this valid and the feminist statement not valid?
Good questions.
These things may or may not matter in an informal debate, but may in fact be a true and valid part of the informal argument as no rules are set forth nor reason given for entering into such a matter in the first place.
I said 'may' because validity is simply what logically follows from the premises. A sound argument is one in which both validity and the truth of the premises is established. Two different arguments may both be equally valid, yet come to mutually exclusive conclusions, because one may be sound (true premises) while the other is unsound (false premises) or one might be unsound while another invalid.
An argument that is not valid is said to be "invalid".
An example of a valid argument is given by the following well-known syllogism:
All men are mortal. Socrates is a man. Therefore, Socrates is mortal.
What makes this a valid argument is not that it has true premises and a true conclusion, but the logical necessity of the conclusion, given the two premises. The argument would be just as valid were the premises and conclusion false. The following argument is of the same logical form but with false premises and a false conclusion, and it is equally valid:
All cups are green. Socrates is a cup. Therefore, Socrates is green.
No matter how the universe might be constructed, it could never be the case that these arguments should turn out to have simultaneously true premises but a false conclusion. The above arguments may be contrasted with the following invalid one:
All men are immortal. Socrates is a man. Therefore, Socrates is mortal.
In this case, the conclusion contradicts the deductive logic of the preceding premises, rather than deriving from it. Therefore the argument is logically 'invalid', even though the conclusion could be considered 'true' in general terms. The premise 'All men are immortal' would likewise be deemed false outside of the framework of classical logic. However, within that system 'true' and 'false' essentially function more like mathematical states such as binary 1s and 0s than the philosophical concepts normally associated with those terms.
Validity is a contextual construct dependent upon its premises and conclusion:
A premise or premiss is a statement that an argument claims will induce or justify a conclusion. In other words: a premise is an assumption that something is true. In logic, an argument requires a set of (at least) two declarative sentences (or "propositions") known as the premises or premisses along with another declarative sentence (or "proposition") known as the conclusion. This structure of two premises and one conclusion forms the basic argumentative structure. More complex arguments can use a series of rules to connect several premises to one conclusion, or to derive a number of conclusions from the original premises which then act as premises for additional conclusions.
The rules of a formal debate dictate how the debate shall be entered into, conducted, concluded, but also how failure to abide by the rules are to be resolved. In a formal debate, decontextualization aids participants' ability to follow the rules (the newly established context), but should a participant 'break' the rules there is a clear course of resolution.
An informal debate has neither a clearly established set of rules to dictate how it shall operate, nor how deceit, biases, errors, or 'cheating' is to be resolved (the forum rules would be the established context for this, but may be too broad and hence informal). This means that not all ad hominem accusations are necessarily valid or invalid or even an acknowledged part of the forum's rules (if so, then there should be clearly established means of resolution or consequence for doing so). The validity or invalidity is entirely dependent on what is entailed by whatever the given premises are, which are defined informally, possibly vague, or even hidden (implied).
Your complaint is simply that you don't want people to make such statements. We might say that this is a valid complaint given your premises (if it were a formal debate). The forum's rules may entail a different, yet equally valid conclusion given different premises.
The rules state to not commit fraudulent activity.
I state that I wish to sell you a particular bridge for a certain amount.
You accuse me of being a con artist and a fraudster.
This is a valid argument with a hidden premise:
You state that particular bridge is a publicly owned property not subject to private sale.
As to the specificity of your question and as an example:
I was once told that 'If you believe in gender equality, then you are a feminist' to which I replied that I did not agree with that. I would rather label myself a gender egalitarian or simply egalitarian than a feminist, i.e. I was using my argument to demonstrate the invalidity of their argument. This is in a certain sense an example of what you were asking for, but it isn't decontextualized by being hypothetical. It has a context that causes it to be valid.