Appeal to Equality example#2 problem

The Appeal to Equality is when an assertion is deemed true or false based on an assumed pretense of equality, where what exactly is "equal" is not made clear, and not supported by the argument.

Here is example #2 with the explanation:

Gay marriage should be the law of the land because gays should have the same rights as heterosexuals.

Explanation: What do the "same rights" mean? Before gay marriage, men had the right to marry women, and women had the right to marry men. A man marrying a man is a different form of the "right of marriage" and needs to be argued as such. Again, there are many excellent arguments for gay marriage, but this isn't one of them.

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I think that Example #2 is not valid for this fallacy because the argument is clearly distinguishing two groups based on sexual orientation and thus it is clear what "equal" here means: "right to marry based on sexual orientation".

Prior to the gay rights movement, heterosexuals did not "right to marry based on sexual orientation;" men had the right to marry women and women had the right to marry men. Gays have successfully (and rightly, IMO) argued that this right should be extended to include the right to marry either gender. Regardless, the main problem here is, in-line with the definition, the claim of equality is not supported by the argument; it is simply asserted.

Let's take a look at my example #1:

If women get paid maternity leave, so should men.

This argument is also clearly distinguishing two groups: men and women and it is clear what equal means: right to paid maternity leave. The problem is that paid maternity leave as it pertains to women (presumably mothers) is not "equal" to paid maternity leave as it pertains to men (presumably fathers). This actual claim of equality is where the problem lies and the two are not equal. There are differences that should be discussed and worked out, not ignored. At the very least, a reason should be provided:

If women get paid maternity leave, so should men because both mothers and fathers need to equally attend to a newborn.

While I don't agree with the above, it isn't fallacious because a reason was provided for the claim of equality (how the two are equal rather than a generic "equal" in every way). We can accept that reason or argue against it.

Gay marriage should be the law of the land because gays should have the same rights as heterosexuals given that gay marriage provides all the same societal and personal benefits as "traditional" marriage and comes with the same risks.

Not fallacious.

Hope that is more clear.