cancel plans without sounding fake or icy

The warmth around the no is doing most of the work

Cancelling in Mexican Spanish has a shape, and it has three parts: an apology, a small reason, and a next step. Leave any one of them out and the message reads colder than you meant. Perdón, no voy a poder, se me complicó, ¿lo dejamos para otro día? is the complete version, and it takes about four seconds to type.

The reason does not have to be a real reason. Se me complicó and me salió algo are both deliberately vague and completely accepted - their function is to signal that something happened, not to submit evidence. Over-explaining is its own tell and usually reads as guilt.

Qué pena contigo is worth knowing because it does not translate cleanly. It is closer to how embarrassing of me than to sorry, and it is what Mexicans say when they have inconvenienced someone they like. On the receiving end, va, no te preocupes and ni modo, para la otra are the standard replies - ni modo being the national shrug for something that cannot be helped.