Is depression part of who a person is? I have been diagnosed with major depressive disorder, commonly known as depression.

Some days ago I had a discussion with my therapist about whether or not depression is part of the person I am. She says that indeed it is and that I should accept it as a part of my being. I should not fight it, but rather accept it. I should not see it as a "demon" trying to mess with my life, but rather as a part of me asking for attention, rising from the dark depths of my mind where I try to bury it. It is a helpess child, my own inner child, crying and asking for help for only apparently no reason, and I should not "beat it up" and yell at it to "go back into its room", but rather ask what's wrong and cuddle it. 

I disagree, as I think that I have depression, but I am not my depression. I'm suffering from a depressive episode, but I am not a depressed person, as I am a completely different human being when I'm not going through an episode. I have an illness, I am not my illness. I might come to terms with the fact that I indeed have depression and that I have to deal with it, but this doesn't mean accepting it as a part of me. I fight it as I fight a flu or a cold. I accept the fact that I have come into contact with the virus, I can't be mad for that, I can't just willingly remove it from my body simply because I don't want it, but that illness is not a part of me, though it affects my everyday life and forces me to feel and act in ways I'd rather not.

You might ask to clarify what I mean with "part of who a person is", so let me try to explain further: is depression part of someone's personality, consciousness, temper, character? Or is it, as a disease, a negative and abnormal influence on someone's regular and healthy behavior? Am I someone who tends to be negative, irritable, hopeless, unexplainably sad and tired, self-loathing, apathetic, suicidal, because that's who I am, or do I suffer from such symptoms of my illness?
Depression can be defined as "a state of feeling sad" (Merriam-Webster), which is an emotion or a feeling in the heart. 

Depression can develop as a reaction to a thought, demand, event or word someone said to you.

You may have a certain "character" or "temper" that makes you vulnerable for things that hurt you and make you sad. So, it is correct to say that you are not depressed as a person but you may be prone to become depressed when something hits you.

Depression is a feeling and not a disease and it usually does not come from an underlying disease, but from the conflicts in your thoughts, attitudes, believes and relationships - which you can accept or change, as appropriate. Depression can make you stop functioning, which you can call a disease, but depression on its own is not already a disease.