Fallacious argument: How could we possibly predict long-term climate trends if we can't even predict the weather a few days from now?
Similar argument: How can we possibly predict the average result of a thousand rolls of the dice when we can't even predict the result of a single dice roll?
The answer, briefly spelled out: We have a pretty good idea of the probability of all the different results of a dice roll. Long term trends are in fact usually easier to predict than single outcomes.
The longer answer: Of course, here I am using an argument by analogy. I implied that weather is like rolling a dice and climate is like rolling thousands of dice. You might wonder if the analogy is valid. It's certainly not a perfect analogy. A dice, for all intents and purposes, always produces a completely random integer between 1 and 6. Weather is a bit more complicated. We may not even know what the probability distribution is, and the probabilities can change from day to day.
However, the analogy is correct in that climate is essentially made up of long term averages and trends in day-to-day weather. In the long term, the random noise will average out over time, allowing the smaller, non-random effects to emerge. The larger the number of days we average, the smaller our uncertainty becomes, not larger. Also, note that consecutive days tend to be correlated with each other. If it's rainier today than usual, there's a higher chance that tomorrow will be rainy too, or that the entire winter will be rainier than usual. Therefore, it's not too surprising if an entire season is, by chance, somewhat different from the long-term predicted trends.
Every time I see this argument, the sheer innumeracy of it makes me want to write something on my blog. Well, there I go. So, do people actually think this is a serious argument, or are they only using it as a rhetorical flourish which relates their climate change denialism to everyday experiences? Who knows? [On the flipside, we cannot dismiss a person's conclusion just because that person used a fallacy. That's what's known as the "fallacy fallacy".]