This quote from General Abizaid came from a roundtable at Stanford University on October 13th, 2007. It was chaired by journalist Carlos Watson, and was entitled Courting Disaster: Fight for Oil, Water and a Healthy Planet. The quote is slightly taken out of context; it was part of a fairly long answer by the General, who was asked whether the goal of "bringing tranquillity" to Iraq was possible in the short-term - but in the context of the claim that the main reason the US was there was to do with oil.
Abizaid responded with the quote in your question, however went on to explain that it wasn't quite that simple, and pointed to other issues such as the rise of Shia & Sunni extremism, the Arab-Israeli conflict, the threat from a potentially nuclear-armed Iran, and Al-Qaeda. I don't think that it's completely clear that this quote came in the context of him agreeing that oil was the main reason for the Iraq War - he could have just been agreeing that oil was part of the reason. He does, however, emphasize the need for the US, in his opinion, to reduce its dependence on Middle Eastern oil.
Below is a transcript of the relevant part of the video, so the reader can make up their own mind.
Carlos Watson: General Abizaid, we clearly have seen... Chairman Alan Greenspan recently said as he came out with his new book that he
thought part of the reason if not the main reason that we're in Iraq
right now has to do with oil and the fight over oil. And whether
that's exactly right or whether the reality is that part of our
involvement in the Middle East is tied to oil dependence, energy
dependence, clearly we're there, clearly lots of troops are there and
many of your own troops have died or been wounded. Give me your
estimation having spent the last four years commanding troops there
about the ability to any time in the near term to bring some
tranquillity, frankly, to Iraq. Is that a reasonable hope over the
next five or ten years, or is it the long war that you've talked
General Abizaid: Look it's... first of all I think it's really important to understand the dynamics that are going on in the Middle
East, and of course it's about oil. It's very much about oil, and we
can't really deny that. And from the standpoint of the soldier who's
now fought in the Middle East for six years, my son-in-laws fought
there for four years, my daughter's been over there, my son has served
the nation. My family has been fighting for a long time, and...
(applause). And the only reason I bring this point up is to make sure
that we understand that this isn't about being a General, it's about
being a citizen. And we have to understand that what's happening in
that region has an awful lot to do with globalization - it's a battle
of the integrators vs. the disintegrators. And the epicenter for the
problem is the Middle East.
Four big problems exist there that our country is gonna have to deal
with for a long time. The first is the rise of an ideological, very
very dangerous movement that's exemplified by Sunni extremism and
Osama bin Laden and many groups that are allied with him. The second
is the rise of Shia extremism as exemplified by a nuclear-armed Iran
which is certainly in the offing today and a state that's very, very
aggressive. Third problem is the continuing corrosive effect of the
Arab-Israeli conflict that absolutely positively needs to be dealt
with, otherwise this continued corrosive conflict drives people to the
extremes in a very difficult way. And the fourth problem has to do
with the need for the global economy to depend upon the flow of oil
from the Middle East. And it is this dependency that we have to
understand can't just be dealt with by military means. We must adopt,
as a matter of national security policy, a way to reduce our
dependence on Middle Eastern oil. It's essential that we do.
Now as we go about dealing with these problems in the Middle East,
there's two accelerators to the difficulty that we face there.
The first is the proliferation of nuclear weapons. And while I used to
lose a lot of sleep over the difficulties of dealing with the security
problems in Iraq and Afghanistan, it was really Pakistan that kept me
up at night. The problem of a meltdown in the society that would cause
a nuclear weapon to go loose, to be transferred into the hands of the
extremists, should be something that we worry about. The other problem
that you need to understand that we're dealing with in the region has
to do with the globalization of the security problems - it's just not
a nation-state problem - Al-Qaeda is not situated in the Middle East,
Al-Qaeda is a global phenomenon, it's a non-state actor, it seeks to
cause its ideology to be spread in the region, and it seeks to do us
The problem for us is that we can't just deal with our problems
militarily, we need to have an economic diplomatic, political
component to the solutions that must not only be driven by the US but
accepted by the international community in a way which allows us to
move forward in a positive way. Having said that, as difficult as it
is, and as difficult as Tom Friedman knows it is, I believe we've got
to stabilize Iraq, we've got to stabilize Afghanistan, we've got to do
our diplomatic best to find some resolution to the Arab-Israeli
problem, and most importantly, we've got to reduce our dependence on
Middle Eastern oil.