The play was correct as he justified what he was worth. The only incorrect move was bringing up "standard of living" as that should only be used when relocating.
That is all that matters - what you are worth and what you think you are worth. If staying in the same area then expenses are immaterial as your out bar has already been set. As an employer, not even a factor.
I've used the "I've got bills to pay" angle as a means to say "You are insulting me". Treat it like buying a car - "c'mon! We've got to keep the lights on in this place! Now what is it going to take to get you in this car you love and make a sale today?"
How can someone be justified and still not have a job?
And for those saying it's just $2/hour, I'd like to know how many got what would amount to $2/hour raise.
But as others have said, your big mistake was doing it through email, but you said that one yourself. Just pick up the phone next time