|Oh, brother. Since your brother is not your keeper, and your job is a keeper, you should certainly not quit to keep him happy. The outcome of two unemployed brothers is only going to make matters worse.|
You do not have to defend your desire to remain in this job, nor do you have to go along with your brother's rants against the company. The best thing you can do for him now is help him find another job that better suits his skills, abilities, and personality. It sounds like he is focusing his energy on having you join him in his misery, while such energy would be spent more productively in updating his resume, networking, and accessing appropriate job search resources, and you can help him do all of this.
Your brother is upset now because his termination is still an open wound, but his distress should quickly subside when he finds a job that better meets his needs. When this happens, he will come to understand that you did what was best for him, and one brother cannot ask another to do more than this.