Part of the problem with explaining the concept of Were's to anyone is that each person will have their own view of things.
I can explain what being a Were means to me and hope that that is OK. I'm sure it will be with all the other opinions you'll get.

My race is Cat Elf. This means that my people are a group whose essences could take one of two forms. My mother/guide/guardian/teacher/mentor identifies herself with the Elf side of our natures. I identify with the Cat side.
I am a Were.
To me that means that I am a Were essence living inside a human body. I do not call it a human host because to me that means that there is a human in here giving me somewhere to stay, playing host to my essence, and that isn't the case. There is just me. Without me the body is empty, just a shell. Without my essence to animate the body, make organs function and eat and drink, this body would die.
Were essences come in various types, shapes and sizes. My particular type is Black cat, which could be Panther or Jaguar as they are names used to identify the same creature depending upon where you live, but which I identify as Cougar as I was originally from Canada in my first life.
I am this Were essence whatever my outer covering looks like, and in each life I can be whatever I choose. Unlike some essences who choose to be several different creatures in their incarnations I stick with one of three bodies to exist in, I choose either large wild cat, small domestic moggie or human. These are the three forms that I am most comfortable taking and living as, so even though I technically could be anything I haven't found a reason to be anything else yet.

For me my essence formed almost with the Universe, and existed for millenia before taking solid form. I was a large black cat before I was anything else, and moved into human relatively recently compared to some.
I enjoy being in a human body, though it has it's drawbacks, it has it's joys and delights too. I enjoy being in a cat body too, though domestic moggie does bring with it some challenges I do not enjoy so much.
Therians are a new invention I have very little knowledge of. I do not understand their viewpoint of this life, and mostly from the views I have read they appear to consider Weres to be vulgar savages without any refinements or sophistication. To them we are the poor uneducated relations, and as you can plainly see some Weres feel resentment toward that opinion.

It isn't personal and it isn't a war, it's just a shame that it has to come to this. Many Therians feel they are superior and look down on Weres, many Weres feel Therians are simply stuck up and pity them for their narrow views. Most Therians hate to be compared to Weres and most Weres hate to be compared to Therians too. I don't think the two will ever come to an understanding as neither side will give on any point, both being stubborn and wilful.

My goodness that's almost my life story, I hope it's of some help.