There's a very significant difference between accurate prediction of the outcome of a random variable vs. measuring the statistical properties of said random variable.
Try this analogy to help you understand this...
Let's play a simple game, called "Pick a Marble". You reach into a bag and pick a marble.
Today, we'll play with the following conditions... There are 1000 marbles in that bag. 100 of those are red. 900 of those are white. I'm going to "predict" that your marble is white. It ought to pretty clear that I'll be correct 90% of the time.
Now, let's play every day. But we'll swap a white marble for red each day. It should be clear enough that in a couple of years I my predictions will change because the nature of the random variable changes. After two years, I'll say your choice will be red and I'll be right more often than wrong.
Weather (i.e. temps two months from now) is far, FAR more difficult than this trivial game. With the most powerful computers imaginable, we cannot predict the outcome of billiard balls past a small number of collisions because the uncertainties in our measurements compound so much over each successive, iterative calculation. Trying to predict weather is far more difficult than that. Even if we had sensors giving us temp, wind speed/direction, humidity, particulates, etc., at every point one-foot apart in a 3D grid of our entire atmosphere, we STILL would not be able to predict WEATHER accurately past about a week... to say nothing of two months.
HOWEVER, it's far easier to treat the weather as a random variable and categorize the statistical nature of such. In laymen's terms, you may not be able to predict the temperature on Christmas Day six months in advance. But you can be fairly confident in suggesting a range.
THIS is why it's fairly straightforward to "predict" the temp (CLIMATE, not WEATHER) 100 years from now while not being able to predict the temp (WEATHER, not CLIMATE) two months hence. And like the changing distribution of red/white marbles, what feeds into the calculations of determining climate is known to be changing over time.
And, though it's a bit harder to understand, this is also why Climate Change doesn't lead to even temp increases all across the planet. The extra energy in the system is monkeying with things a lot turning these nice Guassian variables into weirdness which results in more frequent extremes.