Answer

The topic is broad, and I’ll address it briefly.
First, the authority of the sages applies only in Jewish law, not in aggadah or in other matters. The reason is that authority is not relevant in matters of fact, and I have already discussed that here.
Second, their authority in the realm of Jewish law does not stem from our respect for them, but from the fact that we accepted them upon ourselves (see Kesef Mishneh at the beginning of chapter 2 of the Laws of Rebels). Of course, that does not mean they are not worthy of respect, only that this is not the reason they have halakhic authority.
Third, with all due respect, they were human beings, and people can make mistakes.
Fourth, there are sayings that look like prophecies/promises, but in fact their intent is to say something about the present.
Fifth, there are predictions that make them dependent on some factor (for example: “one who recites havdalah over a cup of wine will have male children”; this is an example discussed by Rabbi Elchanan Wasserman), but there are additional side factors that can affect the outcome (for example, if his wife is barren, or if he deserves punishment for something else), and these can cause the prediction not to be realized after all (that he will not have children). So indeed, havdalah over a cup does affect the birth of sons, but there are other influences that may offset its effect. See much more on this in my article on ukimtot:

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