I could be wrong, but this is what I understood in class. What I'm wondering is it's because he makes the statement earlier that emotions come in opposite pairs? (But I'm not sure he applies that to drives)
By way of preable to answering I'll quote Robert Trumbull's PhD dissertation, online here:
The death drive ... is Freud’s attempt to envision a force present in the living, but antithetical to life, a drive opposed to the drives that sustain organic life. At the same time, Freud views this death or destruction drive as a type of aggressivity central to the formation culture. Tracking Derrida’s thinking on the death drive across his work, I demonstrate how this figure and the notion of “life death” it suggests come to be at the center of Derrida’s engagement with Freud. Through close readings of Derrida’s work, I trace how he reads Freud’s writing against itself, locating there something Freud himself does not entirely think through.
Freud wrote about the death drive, Thanatos, in Beyond the Pleasure Principle. Prior to that he theorised that the pleasure principal motivated behaviour.
Also of relevance in the context is the Nirvana Principal:
Nirvana Principle: Barbara Low's term for the psychological equivalent of homeostasis, the push for the least amount of tension. Different from the pleasure principle in that 1. pleasure sometimes increases with tension, and 2. the Nirvana Principle is primarily under the sway of the death drive, whereas the pleasure principle is powered by Eros.
Freud published Beyond the Pleasure Principal in 1920, shortly after World War I. Mankind going to war contradicted his Pleasure Principle, so he proposed the Death Drive. As it were, an opposing drive.
In fact, the answer lay deeper and connected with his other observations on the repetition compulsion.
As Derrida observes, the root of the repetition compulsion is a deep desire to understand problems. (The relief/pleasure of solving them links to the Nirvana principle.) People are drawn to repeat what they do not understand. It is part of the mechanism that enables a person to master their environment - an essential for survival.
Tenacity and problem solving can spill over into OCD because the drive is deep and not primarily conscious. E.g. the unputdownable crossword puzzle.
Mastery can make a person able to flourish and build, but then again it can lead to invasion and plunder. Historically, and in uncivilised times, this is survival of the fittest. The primary drive for Mastery aligns with the most basic evolutionary principle.
The pleasure principle is not opposed to mastery, however it is subservient to it, in the same way as the pleasure principal is subservient to the Reality Principle. The Reality Principle differs from the drive for mastery in that is it more conscious and deliberative.
The death drive is one name for the drive for mastery. Another would be the war drive, or contrastingly, the civilisation-building drive / culture-building drive.
It is only because it is more complex than the pleasure principle that is can appear to oppose it, for example when it provokes war, or simply when the unputdownable crossword puzzle drives you to distinctly unpleasureable distraction.
The death drive is largely symbolic. It addresses the fundamental incompatibility of positivist logic (the reductive, particularizing logic of psychoanalysis and other scientific discourses) with the ambivalence of the human psyche (and, arguably, the universe at large). Freud gives us the death drive to simultaneously compliment and oppose the life/sex drives (Eros) long accepted by psychoanalysis as the motivating forces of human existence (all life on earth, actually, but most specifically human life). The symbolic dualism of Eros and the death drive (which Marcuse personifies as 'Thanatos') is simply meant to stand in for the ambivalence mentioned above. The death drive doesn't manifest in isolation because it exists in fusion with Eros--in a kind of flux-equilibrium. Even if it did, it wouldn't pursue real, bodily death, but the deconstruction of the 'self' (psychic death--the death we truly fear and awe).
In my opinion, something as simple and common as the urge to drink heavily--to pursue and enjoy drunken 'oblivion'--is a worthy example of the death drive. There you can imagine an admixture of Eros nagging from the back of the brain, "regulate, be responsible, beware hangover!", and then another little deathly voice tempting "just one more shot, what's the harm?".
Of course, our thoughts don't pass quite so neatly. If we really want to liken the drives to a voice in the mind, we should imagine a little bit of each drive contributing to one unified voice.