In the most recent episode S02E12 of Star Trek: Discovery,
Tenavik told Pike that if he could choose to walk away from the future he saw and if if he took the time crystal, his fate would be sealed forever.
How exactly does it work?
Science Fiction & Fantasy Stack Exchange is a question and answer site for science fiction and fantasy enthusiasts. It only takes a minute to sign up.Sign up to join this community
Now that we've seen the finale, I think this question has a logical answer.
Taking the crystal is a necessary pre-condition for defeating this season's antagonist. By taking the crystal, it is possible for the Discovery crew and Pike to solve all of the problems that led them to this point, which means that Pike's story continues as we expect it to based upon the Original Series, e.g. the vision Tenavik talked about becomes true.
The alternative to defeating the antagonist has been stated to be the complete destruction of all known intelligent life in the galaxy. Indeed, later events in the finale show that without the time crystal,
The entire plan to stop Control would have failed, with Discovery and Enterprise destroyed in the final battle or before it, because Burnham would have been unable to guide Discovery to collect all necessary plot tokens (Reno, Kelpians, the time crystal, the Klingons, Po) to win the battle by being the Red Angel who created the Seven Signals they were looking for in the first place.
In that case, Pike would have avoided the future that he was shown by Tenavik because the Federation would likely not exist, or Pike would have died sooner, so he would not be able to have the future we already expect him to have based on the Original Series.
So the trick here is that Pike is shown the good outcome in a very misleading way that looks very bad for him. Pike is not shown the alternative, which also would have been bad for him, but in an entirely different way.
Star Trek Discovery is a prequel series, and Pike's future as seen in the vision given by the time crystal, has already occurred in Star Trek:The Original Series, in The Menagerie Part One and Part Two. These episodes show exactly what eventually happens, that Pike saw fragments of in the vision.
As it seems the events of ST Discovery are canon for the main Star Trek universe, Pike now knows part of his own future but is probably unwilling to tell anyone and risk damaging the future.