How about questions like "Why did the Big Bang take place?" or "Why is there anything?" Do you think science can answer those questions? Are they pseudo-questions, as many cosmologists say?
I guess it depends on the type of answer the questioner is expecting. If they're expecting to hear about some proposed deeper underlying mechanism for the Big Bang taking place or for there being anything, then we could say that what they're really
asking is not a "why" question but a "how" question (in the sense that those two words have been used in this discussion.)
But if they're expecting something else then they need to specify what kind of information they're after. Otherwise the person they're talking to simply won't know what they're asking and might indeed accuse them of uttering a "pseudo-question" - i.e. a form of words that sounds superficially like a question but which on closer examination turns out not to be. In that case, it's not just science that can't answer. Nobody can. If it's not a question, it's not a question.
-- Updated Wed Sep 13, 2017 9:29 pm to add the following --
I suppose one technique that people sometimes use to answer these things that seem to be pseudo-questions is to simply answer a different question. So if I ask somebody "why are we here?" they might answer with: "to love each other" or "to develop to our full potential as human beings" or perhaps "to praise God and His glorious creation!".
In that case, the question they appear to be really answering is: "what activities do you attach most importance to in your life?"