Who am I? What am I?

Talked with my therapist the other day about defining who I am. What characteristics am I most proud of? What do I want people to see me as?

This left me upset and wondering for hours. It seemed as if the therapist was suggesting that I don't have something clearcut, but that doesn't really make sense. We ran out of time just as I finished naming things. So I'm just kind of flushing out ideas that I talked with him about. I didn't know if they were suggesting I was doing too much and taking on too much, or whether I need a clear cut single hat that I wear and that's me.

A dedicated friend who will go the extra mile for you, is there to listen, and support.
A son/family member meaning I'm there for my dad in this difficult time, and do so much to help out (taking dad to doctor, cooking dinner, handling stuff related to my grandma and aunt, there for my family in hard times).
Teacher who supports the students making sure they are comfortable in the classroom setting/create a positive learning environment.
A gay guy who is more or less comfortable with himself and those knowing, even though it has cost me friendships (like The Mike's).

Characteristics:
Quirky- I don't take myself too seriously and I tend to say what is on my mind, which may come out quirky. Is this a bad characteristic?
Bitchy/sarcastic- I can go from 0 to bitch in 3 seconds, can you? Piss me off and I can be someone you don't want to cross. I can also just be bitchy to be funny.
Serious- I know when to be serious and when to not. Sometimes I think I'm too serious, but then I question my quirkiness and wonder if I'm not too quirky and not serious enough.
Mature- Able to handle tough situations (stuff with aunt, dad, etc.)
Studious- Good grades, good GPA, [somewhat-it varies] dedicated student
Caring- I care deeply, and I know I sort of have that guilt persona where I worry so much, and part of me worries about hurting those around me because I care.
Dedicated- will get it done. PERIOD.
Adventurous- I like to try new things, go new places, try new foods, and will try most anything once.

Was the therapist saying I take on too much? Is it about how friends/people perceive me? I just know that I was really bothered and after a couple days it still is something I'm questioning. I think another thing is that I'm wondering how people see me, especially with the loss of Mike and other friends. Yes. I know, get over them because they're not good friends. I feel that I am over, but I just wonder and am questioning what I am, who I am, my flaws, what I need/want to change/work on. I think part of the reason I am posting this is I do want some feedback/am curious to know what people think since it has bothered me this much. I know I'm opening up myself to a lot of potential ridicule/people telling me I'm a good guy, don't worry, by doing this, and I know this is one sided, you just getting my thoughts, so it is not objective, but I am curious as how I'm perceived. Do I have flaws?

I think there needs to be a balance between quirky and serious. I think I match that pretty well. At work I know when I can choke, be funny, less serious with a kid. I know when I need to take control and lead. I can do this in the classroom setting when I'm a student and there is a teacher. I can be serious when needed when dealing with family stuff and less serious 95% of the time. I am not business 100% of the time. I just know I think how to act when in the right situation and deal. I think the bitchy just adds to the mix. It is fun. It is me. I think I'm fine not having a single clearcut, wonderful, shining characteristic. This is what makes me unique.