- AFAIK, no one knows absolutely for sure, but...
- We can be safe to assume it was to be politically correct.
- Without trying to turn this into a debate about "PC Police"...
According to Wikipedia:
- The original phrase was introduced in August of 1966.
- Political correctness was in full swing by the 1980s.
- The modified version was used in 1987.
- By the mid 90s and early turn of the century political correctness research was in full swing.
- The original phrase was reinstated in 2009 with the reboot films.
So while I can find no real confirmation (from official sources) we can be safe to assume the change was made with the idea of being politically correct. There are a lot of Google results that debate this topic and Google will even auto-complete the search when you type it in. Just about everyone is in agreement of why the change was made, but as I said, I can find no official statement to the fact.
Also, given the amount of time that has passed since the changes were made it is unlikely we ever will hear an official statement. Conjecture and inference are our only allies here.
So it is very likely that attempting to be politically correct the powers that be modified the introduction in an attempt to not seem gender biased. Of course, changing 'man' to 'one' makes the show inclusive of the idea that women are fully capable of exploring other worlds too.
By the middle of the 1990s the battle over political correctness was very much in full swing and the idea had been warped and weaponized. The bulk of the research appears to have begun to emerge around the early and mid 2000s with the ideas of being 'PC' both good and bad. Still today there is new research being done about the topic and attempting to determine if its effects are more of an improvement or determent to our society as a whole.
With the release of the new reboot films in 2009 and 2013 the introductory phrase was returned to its original. I can not find any official reasoning for this or who made the decision. Since the original change and more recent reversion the two camps have persisted. One side holding to the idea that the original phrase is sexist and the other to the idea that 'man' has always meant 'mankind.'
Quite honestly, it means what we as society deem it means. Words and meaning change throughout history and always will. For me, I have always read the phrase as 'humanity' and the idea that the human race is exploring among the stars... obviously there are already other man and woman genders out there in the Star Trek universe... they are just of different races...