Beg pardon, but that's not quite answering the question. Having or not having confidence in flying abilities is one thing. Being brave enough to admit it, another.
I know an ex-RAAF pilot who is obsessive about safety. The sort of guy who checks everything three times. Decades of experience. I think if he was uncomfortable about flying in certain weather conditions, he would admit it, whereas a younger guy might not.
While I would prefer my pilots to be experienced and confident, I also want them to be honest rather than foolhardy. I notice some planes diverted last weekend, and I'm guessing that was weather-related, and the pilots accepted that in a highly visible way.
I guess the question might be rephrased as "when does an airline pilot admit that the weather is beyond the abilities of himself or his aircraft?"
I am sorry you thought I was not answering the question - now that I am back home on a desktop computer I can give a more thorough answer.
There are strict limits for aircraft with respect to items like crosswind and visibility for takeoff and landing. The aircraft is certified to a set limit, so you don't go over it unless in an emergency situation. Simple as that. The limit is also a certification demonstrated limit - that doesn't mean that every pilot is capable of operating right up to that limit. In that case, the operator may impose more stringent limits - for example, the demonstrated crosswind limit might be 35 knots, but that may be reduced in wet weather, on narrow runways, when some items like thrust reversers or spoilers are unserviceable, or when the First Officer or new captain is flying. Those limits would be found in the operations manual for the operator.
Visibility for takeoff and landing is a set figure - you either have it, or you don't. You also have contingencies in case the visibility reduces after you have commenced the procedure - for example, we have an additional low visibility briefing in the flightdeck in low vis takeoffs that includes actions to take if the visibility reduces at high speed before rotation.
So as you can see, there are stringent requirements that must be met - and the training trains to those limits. You don't just get thrown in an aircraft and try your first maximum crosswind landing unsupervised - it just doesn't happen (at least in Australia).
There are of course times when the limit is beyond the abilities of the crew or the aircraft - and then it comes down the crew. Decision making processes are trained for and assessed - holding airborne or delaying on the ground due to the inclement weather, picking who will fly the approach and how the crew will operate or choosing an alternative route are all options that are considered in periods of bad weather.
We are all obsessive about safety - or we wouldn't be in the airlines. I don't think many pilots in RPT operations in this country are 'fool hardy' as you put it - there is just no place for that with passengers down the back. Yes, being uncomfortable does happen (severe turbulence is never fun, nor is serious windshear on takeoff or landing) - I generally won't be acknowledging it airborne because I will be managing the situation with fairly high workload. But I am all for a debrief on the ground with the crew as a discussion point.
