Ezra Taft Benson said virtually the same thing. How have LDS prophets led members astray? Before you attempt an answer, you might wish to reflect on the fact that Pres. Harold B. Lee, who opposed granting the priesthood to all worthy male members, had--with Pres. Howard Hunter--the shortest term of all the prophets that preceded him (1972-1973).
Why is it that errors in judgment by scientists ("I can see a need for five computers worldwide at the most") are excused because science is self-correcting, but the same latitude is not granted to LDS prophets? Is it not true that BY's errors were eventually corrected by the prophets that followed him?
Your rejoinder will be that LDS prophets claim to receive communication and direction from God, and God is never wrong. True, God is never wrong, but those called to do His work in mortality are not infallible; i.e., they are, indeed, sometimes wrong.
I'm not following your line of argument. It seems to be taking several positions at once, hinting both that Woodruff's proclamation was true because of a couple short terms by prophets, and that it was false because prophets are indeed fallible and can lead the church astray.
So I'll just make several unconnected responses to the various points:
Either refusing the priesthood based on race was correct for over a hundred years, or God did let prophets lead the church astray for several generations. The D&C says, "The Lord will never permit me or any other man who stands as President of this Church to lead you astray... If I were to attempt that, the Lord would remove me out of my place..." That's crystal clear that the
current prophet would be removed, not a future one a century later.
The fact that some prophets had a short time in office seems pointless cherry-picking, when Brigham Young had a long time in office. There will naturally be a random variation in lifespans and a human tendency to find patterns in randomness. The fact remains that church presidents successfully kept blacks from having the priesthood, despite Woodruff saying God would not let the president lead the church astray. If one accepts Woodruff's statement as true, the obvious conclusion as far as I can see is that the church was
not "astray" at that time and that God
did feel blacks should be banned from the priesthood until 1978. It's politically incorrect, but it's a more logical consequence of accepting the D&C as true, than claiming that the church was being led astray all those years (which requires believing that Woodruff was leading the church astray when he claimed the church could not be led astray).
Errors in judgment by scientists are accepted because scientists don't make claims that they're either infallible or will be removed from power, like Woodruff did.
The idea that morals are self-correcting doesn't really make sense, because morals differ from a shared reality. A scientist in another culture can replicate an experiment and if the controls are the same, the result will be the same. But how does one design experiments to falsify "lying is morally wrong?" or "gay sex is a sin"? The most one can do is make other claims: "In this culture, most people think..." or "Under these conditions, it causes this specific benefit and this specific harm..." But without an objective definition of morality or sin, there's no way to "self-correct" to get closer to what actually is moral or sinful. That's why preachers make proclamations which require faith.