Why do we rely on others in dangerous situations? *This question is based on my observations.

Q: What is the reason people trust their peers implicitly in extreme (or not) situations?

Example:


  I am walking with a friend, and I am telling him something. Now we need
  to cross a road to the other side (not at the crosswalk; we both
  know that, so this fact is not communicated – we just proceed to the
  other side) while I am still telling him something. Unconsciously
  I understand that we are crossing a road at this point, and I am aware
  of the possible dangers even at that same point when I am thinking
  about it, but still I do not look to the right or left and continue
  following my friend, putting my well-being on his shoulders for that
  moment.


This may not be the worst case scenario and maybe not so extreme, but it is imaginable, and such a pattern is common in many different situations when one person relies on others' awareness of the dangers the current situation possesses without analysing and watching out for such dangers himself, thus dismissing the self-preservation instinct.
Q: What is the reason for people to implicitly trust their peers in extreme (or not) situations?


Reliance is basically the dependence or trust in someone, to each lies a limited capability of being relied on due to our limited capacity as human beings. What I'm trying to imply is that your friend might have been able to consciously lead you across the road without you questioning his judgement, but in a time of crisis would you let that same friend tell you that it's best to invest all of your money into a shoe shining company? 

We depend, or rely on specific people for specific things. Growing  up we rely on our mother to provide us with the maternal support and experience required, just as we rely on our father (or father figure) to teaching us what it means to be a man. (Assuming the example human is a male..)

If you were a CEO of a huge company, you would have no trouble relying on your employees to do a specific job in which you ordered them to complete, but only knowing them on a work-basis what are the chances of you trusting them to the extent of looking after your children for a week while you're on holiday? (Also assuming the example human is a parent..).

Trust is a huge factor in the concept of persuasion, and to pursuade someone is to induce someone to do somthing through reasoning or argument. You are more likely to be pursuaded by someone whom you trust in, rather than someone you don't. That person you have relied on has shown to prove the actuality of being credible and knowledgable in the field in which you have decided to trust them in, thus allowing them to lead or guide you as an authority figure.

Also, childhood experience highly influence who we trust and to what extent, but that is an area in which I have little knowledge available to answer you question. I hope I made my message clear. Nonetheless, these are based off of opinion, although @denniswennen had a similar argument.