Use this when you want to say how someone thinks or acts: in a way that does not follow from the facts or from good reasons. It tells you the manner, not the thing itself. It sounds a little formal. Friends more often say “for some reason” or “that doesn’t make sense.” Though actually people also use it lightly, almost with a laugh, when a choice is silly rather than strictly false — she illogically bought another pair of shoes she will never wear.