So it was necessary to say that pus is made of somatic cells to explain that the claim is in fact true.

And so is liver, and intestine, and heart, and skin, and lungs, and bones, and blood, and most everything else in a living creatures body.

You are trying to hide behind a technically because you know the whole “MILK IS FULL OF PUS AND BLOOD” is bullshit. So you keep dancing around the edges, saying somatic cells are pus cells, saying pus is made of somatic cells, trying to trigger a revulsion in the ignorant who don’t know what they even are.

You are trying to do the whole " All people who consume Dihydrogen Monoxide eventually die, highlighting its toxicity" type spiel.