You can put this solution on YOUR website!
That statement is unreasonable for a number of reasons. A 100% chance of something happening means that the thing will happen with absolute certainty. As in the statement, "Every human being has a 100% chance of being dead someday."
So let's express the conditions for your question slightly differently. If there is a 60% chance that it WILL rain on Saturday, that means that there is a 40% chance that it WON'T rain on Saturday. Likewise, there is a 60% chance that it WON'T rain on Sunday. Using the logic of the statement under discussion, that means that there is a 100% chance that it WON'T rain at all that weekend. Hence, if the given statement were true, then my equally ludicrous assertion must also be true, but how can it be absolutely certain that it WILL rain and absolutely certain that it WON'T rain all in the same weekend?
Consider a fair coin with heads on one side and tails on the other. If you flip the coin, you have a 50% chance of it landing with the head up. Using the logic of the given statement, if you flipped the coin twice, heads must certainly come up at least once. Try it a few times -- the first time you flip two tails in a row, you should be convinced.
You could look at one of a pair of dice. A single die has the numbers 1 through 6, each with a 1/6 chance of being on top when the die is rolled. By the logic of the given statement, if the die is rolled 6 times, each of the numbers has a 100% chance of showing up at least once. That means it is certain that every time you roll one die 6 times, you will get one of each number. It won't take many trials to disprove that claim.