What is the importance of human relationships? Why do we need people? After all, we are born alone and we die alone?

Relationship is the way in which two or more people or
things are connected, or the state of being connected.

One of major foundations of the system that governs us has been the fact that we are highly dependent on others for our survival. The first instance in our lives where we can clearly notice this dependency is the time of our birth, we are born inside a womb and are depended completely on our mothers every bit of nutrition that we receive at that early stage when our body is being constructed. Although in a way, we are highly independent when we die but then there still remains a good deal of dependency for the final rites of our dead bodies.
So, what really am I trying to say here?I think the only aspect that beautifies this system of dependency that governs us is 'relationships'. When we as human species create connections with our fellow humans we invite endless possibilities in our life experiences. 

Can someone live with no relationships with his or her fellow human beings? 

Yes, of course. But then what kind of a Life will that be? Specially if we take into consideration that we as humans have been made with an inner predilection towards others who share this planet with us, the matter becomes clear from confusion.
Personally, I think of a Life with no relationships, as incomplete and here are some reasons why relationships are important -

1. We learn and evolve not just using textbooks and applying our knowledge in our work or by merely responding to our inner calling. True learning and evolution includes the art of dealing with a variety of people 
2. People play a crucial role in our lives, sometimes they put a smile on our faces when we have forgotten about it. Sometimes, they make us feel depressed too. In either case, we become strong and that is what matters at the end
3. To be human is to love others for who they are. Without relationships we are bound to feel empty (Of course, it is a different matter altogether that some people in order to support their belief about being isolated, would never show how empty they feel within)
4. Finally, we need to accept that emotions dominate over logic and that makes the whole difference in the way we deal with people. Emotional needs are critical and they need to be given priority. If I were to make a list of 'things' that are a source of emotional satisfaction, with no doubt, human relationships would be among the top three if not on the top itself