It is because of Men the Ring survives.
5 seconds sound clip from the The Lord of the Rings: The Fellowship of the Ring movie soundboard.
You can hear this line at 01:31:47 in the Blu-ray version of the movie.
Quote context
[...]
- The time of the Elves is over. My people are leaving these shores.
- It is in Men that we must place our hope.
- Men? Men are weak. The race of Men is failing.
- The blood of Numenor is all but spent, its pride and dignity forgotten.
- It is because of Men the Ring survives.
- I was there, Gandalf. I was there 3000 years ago...
- I was there the day the strength of Men failed.
[...]