"He has a shirt, but it is not red."
Translation:Αυτός έχει ένα πουκάμισο, αλλά δεν είναι κόκκινο.
Because the pronoun is actually implied. You are talking about the shirt, so you could actually just ommit αυτό, or εκείνο. It's not wrong, it's just not a necessity. :) Unlike english, because if you ever said "He has a shirt, but is not red" it doesn't sound nor is correct. xP
Good question. :P
I'd say it's one of those things that just sounds more natural. In my (native Greek) head, I can imagine this sentence in a dialogue similar to this one:
"I really want a bag that matches my dress. Do you have one I can borrow?"
"Well, I do have one, but it's not red."
It would just sound a bit more unnatural to just say "έχω πουκάμισο" instead of "έχω ένα πουκάμισο", in that context. Then again, it could just be the force of habit that natives usually find themselves affected by :P
However, the alternative without ένα is accepted. ^.^