Not a Teacher(Perish the thought!)
To take moments seems to be a derivate from much commonly used phrase to take a moment (to do something). Simply to find a momentto do something.
In the evening, we took moments to sit and talk together.
During our climbing the mountain, we took moments to stop to look around.
The night shift was tough, I was on the go all the time, but I was able to take a moment to eat something.
But in the context of the paragraph it sounds really strange and I do not pretend to know what exactly it means, though I have suspicion it may be something like, Though we are considered to be a leader we are not sure if it is really so.
Hopefully some good native speaking soul will emerge to enlighten the problem for you. J
P.S. Here is the text by the guy who uses it in his lessons.
Student or Learner