Welcome to the forum!
I think this part of what you've said really stands out to me, "He said he still has love for me and he is still looking out for me despite not wanting to be with me.I am not sure whether I should carry on fighting for us to be together or whether he is actually better off without me. "
I found that reading your post reveals very little about you or how you feel, it's all about him and about what's best for him. Clearly, you are a very caring and loving person, but I wonder if you are valuing your own needs and wants here. Do you really want to be with someone who has made clear that he doesn't want to be with you? Who was emotionally distant at a time when you needed support?
It may well be is actions towards you are the result of his depression (self-destructive, unclear feelings, low self-worth), but that doesn't give him an excuse for this behavior. It doesn't mean you have to forgive or explain away this behavior, particularly as you've only been dating for a relatively short time. You also can't fight for a relationship that the other person has said they don't want to be in.
My advice would be to think more about your own feelings and needs. This person has decided to end their romantic relationship with you, I would advise you to try and accept that decision and focus on yourself for awhile.
All the best, V