It is easier to inadvertently take-off with ice than generally accepted. As pax in crew bus to stand-off bay I checked surroundings for ice. None on aero bridges, trolleys, various tugs and other vehicles. Couldn't see ice on other aircraft as we drove, or on the tarmac. Nobody was de-icing before departure etc etc. It was a fair bet that there would be no ice on my A321.
I looked for ice during a slow and careful external check. No visible ice. As best able I looked through each open cockpit window at what I could see of the wing leading edges. Looked carefully through the over wing emergency exits and other pax windows. Still no ice. But there was still one duck to line up, so I opened the aft galley door and had a good look at everything I could see from there. About to call it a satisfactory check and decided that while there I would also check the left horizontal stabilizer.
There was sufficient clear ice there to cause concern. In all cases, any is unacceptable. We were critically questioned about our need for de-icing by my culturally conditioned airline, but of course I insisted.
Except for my local F/O, who trusted my decision, there was not a single person who believed we just saved an aircraft and over a hundred lives by insisting on de-icing. The problem with such situations is that the de-ice equipment is not fully staffed, schedule will be disrupted, crew duty hours may be a problem with no replacements available, the cost of the de-ice, and most significantly, the loss of face when competing airlines depart without de-icing.
So while the principle of no ice, holdover times and so on are clear, there are multiple considerations that together conspire to reduce our confidence in the need for de-icing. As pilots, we are absolutely required to follow all the procedures needed to keep our aircraft airworthy.