The speaker sets up a pattern of three situations, and the third one breaks it. In the first two, the illness is physical and frightening: a gangrenous leg, then a liver that grows teeth and hair and tries to take over the body. In both, the speaker trusts "you," a friend or loved one, to give the hard but sensible advice: cut it off, remove it. The images are grotesque, yet the tone is calm, almost matter-of-fact, because the answer is so obvious.
Then the job arrives, and it is described as something choking the speaker, with hands around the throat. Here the "you" suddenly changes sides, warning about "career suicide." The phrase is bitterly ironic, since the speaker is the one being strangled. The mood shifts from dark humor to quiet frustration and disappointment. The poem suggests that people will happily support us in cutting out a diseased body part, but struggle to accept that a job can be just as harmful, and the speaker feels unheard.