“Because superior non-animal methods are used for this exact training by military and civilian programs around the world, animals are clearly not required to meet your objectives. … I'm sure you agree that our military personnel deserve state-of-the-art training and that our country deserves to be respected for its civilized treatment of animals.”

De Re Militari (also Epitoma Rei Militaris), Book I, "The Selection and Training of New Levies"
Context: Victory in war does not depend entirely upon numbers or mere courage; only skill and discipline will insure it. We find that the Romans owed the conquest of the world to no other cause than continual military training, exact observance of discipline in their camps and unwearied cultivation of the other arts of war. Without these, what chance would the inconsiderable numbers of the Roman armies have had against the multitudes of the Gauls? Or with what success would their small size have been opposed to the prodigious stature of the Germans? The Spaniards surpassed us not only in numbers, but in physical strength. We were always inferior to the Africans in wealth and unequal to them in deception and stratagem. And the Greeks, indisputably, were far superior to us in skill in arts and all kinds of knowledge. (Book 1)

Kissinger has denied saying it.
The only evidence that Kissinger ever said this was a claim in the book, The Final Days, by Bob Woodward and Carl Bernstein, in chapter 14 (p.194 in the 1995 paperback edition). Woodward & Bernstein claimed that one of Kissinger's political foes, Alexander Haig, had told someone unnamed, that he (Haig) had heard Kissinger say it. That's triple hearsay, made even weaker by the fact that one of the parties is anonymous. Kissinger has denied ever saying it, and it was never substantiated by Haig, nor by anyone of known identity who claimed to have heard it. As Kirkus Reviews noted about the whole book, "none of it is substantiated in any assessable way."
In fact, the quote is not even very plausible, on its face. Kissinger served with distinction in the U.S. Army during WWII, and was awarded the Bronze Star. He has always been very respectful of other servicemen and their sacrifices. For him to have said such a thing would have been wildly out of character. In fact, the awkward phrasing doesn't even sound like Kissinger, whose English prose is consistently measured and careful, despite his heavy accent, even when he speaks extemporaneously.
Misattributed

2012, Yangon University Speech (November 2012)
Context: And to protect the freedom of all the voters, those in power must accept constraints. That's what our American system is designed to do. Now, America may have the strongest military in the world, but it must submit to civilian control. I, as the President of the United States, make determinations that the military then carries out, not the other way around. As President and Commander-In-Chief, I have that responsibility because I'm accountable to the people.

“Young Actors Visit a Rescued Animal Sanctuary,” video interview with PETA Kids (14 November 2016) https://www.youtube.com/watch?v=-jq4n3Pnku0.

Bewilderness: New York (audio CD, 2002)

Source: The Book of Pastoral Rule, p.62

Source: blog, 28 June 2007

Speech at the National Press Club (2004)