I think much of what we are being told about Parseltongue is a lie.

What we've been told: Parseltongue is the language of snakes. Because snakes cannot lie, Parselmouths also cannot lie in Parseltongue. Salazar Slytherin invoked the Parselmouth Curse on himself and his descendants to take advantage of this last fact by using it as a trust engine.

However, snakes have no spoken language. This is a fact established by Muggle science. So what is Parseltongue, really?

Parseltongue has four confirmed functions.

• 1) It can temporarily awaken snakes to the level of human intelligence.
• 2) It can compel obedience from any snake so awakened.
• 3) It enables two-way conversation with any snake. This seems to be a passive, area of effect feature, as Draco's Patronus speaks to Harry in Parseltongue without any way of knowing in advance that Harry will be able to comprehend it.
• 4) It prevents the speaker from knowingly making false statements.

Note that 1,2 and 3 are thematically unrelated to 4 (given that one does not expect a snake to lie, and in any case can order it to speak the truth).

Suppose the wizard S (possibly Salazar, possibly not) creates a spell or ritual that makes one a Parselmouth. Is it likely that they create a magical user interface for controlling snakes, and then decide that it also needs to prevent the user from lying?

On the other hand, suppose S has created a perfect trust engine. They decide, as we know, not to make this information public, either in order to preserve an advantage for themselves and the allies whom they will teach the spell/ritual, or because they fear the chaos doing so would bring (every deceitful person would wish it destroyed, while everyone who fears being deceived would want it made universal), or both.

They then conceal the trust engine inside another, separate ritual, which grants the power to understand and command snakes. Even if such a ritual becomes known, people generally aren't bothered about the ability to command snakes (which are a low-status animal anyway). Nor will they see anything strange about Parselmouths using their speciality language to communicate securely with each other. If S is Salazar Slytherin, he also has perfect cover for why he'd want to create such a ritual because the snake is already his personal symbol - or perhaps he adopts that symbol after creating the ritual, giving himself and his descendants a plausible reason to be Parselmouths.

So why is the ritual known, according to Voldemort, as the Parselmouth Curse? There are no downsides to the power to understand and command snakes. But if S or one of their successors calls it a curse, that radically reduces the number of people who might seek to learn and use it.

P.S. One obvious argument for Parseltongue being a language is that being a snake animagus supposedly lets you speak it without being a Parselmouth. However, we don't actually have any evidence for this - Quirrell is a Parselmouth already, so his ability to speak Parseltongue in whatever form is not a test that behaves differently under different circumstances. His statement that a snake animagus is not the same as a Parselmouth only supports this observation.