I'm a graduate student who gets paid in pretzels. I wish I could use the tax credit for my fees and get a max of $1,000 back.
ANSWER: I see your point, but policy-makers seem to feel that a BA is the new high school diploma and until they get everyone up to that level, they won't be offering tax breaks for advanced degrees.
Additionally, they probably think that it is more in the public interest to get someone with a BA out in the marketplace producing something of value, rather than paying them to become a higher-priced consumer. Graduate degrees can be immensely useful to society or they can mostly just benefit the individuals who have them.
If a college tax credit for graduate degrees was offered selectively, it would be perceived as unfair and could backfire with unintended consequences.
The goal of a tax incentive (from a policy standpoint) is not to benefit individuals, but to benefit the economy as a whole. With any college tax break, it is a question of whether it is worth getting the delayed benefit of a higher-skilled worker, compared to the immediate benefit of a lesser-skilled one. I guess it works out as "yes" for the four-year degree, and "no" for the additional two to four years.
(Incidentally, you can see this philosophy at work in the administration's decision (supported by Congress) to eliminate the graduate subsidized loan program. While there are undergraduates with no degree still paying unsubsidized loans, it doesn't "seem" fair to policy-makers, that any graduates should get subsidized loans. It's not really a rich vs. poor thing; more of a haves (B.A.'s) vs. have-nots.)