Always or absolutely most often very educated and professional partners I speak with talk about consistency (ie we shouldn't be able to prove something that is false)...Yet I suggested somewhat of a counterexample. Lying about everything seems to be "consistent" but not congruent. Therefore I suggested that we should speak of congruency when talking about language when consistency seems to be more about pure logic. Could we elaborate on this topic a bit since still much more emphasis is on consistency than congruence? Thank you
To what context(s) is your question meant to apply?
By strictly observing the way your question is tagged, I assume you meant to talk about programming languages in general. But I rarely see programming languages talked about in terms of consistency, and in fact, I struggle to understand how your example (this idea of a binary truth-falsity divide) is at all applicable to the design of programming languages.
In general, yes: logicians might talk about both consistency and congruence. But it's far more important that subjective standards like design patterns, coding standards, and even language architecture/design be consistent, since there is no universal or "correct" way of implementing them.
Beyond that, I'm not sure how congruence solves your counter-example of lying. Certainly there could be agreement on a lie, or any type of false premise. Even with the abstract definition of congruence as similarity between objects, I see little justification for a consistent lie's lack of symmetry.
Certainly we could have a lengthy discussion about the nature of Truth in general, and its specific relation to formal logic, but that would be clearly off-topic here.