For example, they think that “can I sit down? ” and “may I sit down? ” are the same. A misconception (un concepto erróneo). Part of the problem is that many English people make this mistake, perhaps unthinkingly (irreflexivamente), and because you hear it often, you assume it is right. Wrong!
Remember that for many centuries people thought the world was flat! That did not mean that this was correct.
Let´s get to the nub of the issue (vamos al quid del asunto). Can (poder) is about the ability or capacity (la capacidad para hacer algo) to do something.
For example, the statement that Mr. Rajoy, the Spanish Prime Minister, and Miss Ester Cuni, Tenerife web designer, can play the piano is about their ability to play the piano. If I asked you whether you can speak English, then the answer may be yes or no or a little. This has nothing to do with permission – only ability. So to the question “can Javier fly a plane ” the answer is about whether he has the ability to fly a plane, not whether (or not) he has a licence to do so.
So “can I sit down” (if you are asking another person) is a stupid question.
Why would you ask someone if you had the capacity or ability to do something? You should know the answer. So why ask the question?
“May I sit down ” is asking for permission. There is no other option for the well-spoken (buenhablado).