Taharos, Chapter 9, Mishnah 5. This chapter follows the olive through the stages of its production and asks, at each stage, whether the olive has yet become susceptible to tumah. Our mishnah presents two separate cases: olives left to soften, and olives cracked open by hand.
"Hamani'ach zeisim bakutash sheyimasu." A person places his olives in the press so that they will soften and be easier to crush when the pressing begins. "Harei eilu muchsharin." These are rendered susceptible to tumah. The liquid that seeps out of them while they sit there counts as a liquid that prepares them, because the softening is part of the work of producing oil.
"Sheyimasu sheyihyu melachim." Now change the purpose. He is not softening them in order to press them at all, but in order to salt them, the way one prepares olives to be eaten. Here the Tannaim divide. "Beis Shammai omrim, muchsharin, uBeis Hillel omrim, einan muchsharin." According to Beis Shammai they are susceptible; according to Beis Hillel they are not.
The Bartenura frames the argument around the mohal, the watery juice exuded by olives. In the view of Beis Shammai, that moisture does render the olives susceptible, for in their opinion the processing of these particular olives has reached its conclusion. Beis Hillel counter that no susceptibility takes hold, since to their mind the olives' labor remains incomplete: reaching the point of salting is not yet the finish of what needs to be done with them.
"Hapotze'a zeisim beyadayim teme'os, tim'an." A person cracks open olives with his hands in order to eat them, and his hands are tamei. He has thereby rendered the olives tamei. The mechanism is worth following step by step. Hands that have not been washed and purified carry the status of sheniyos. When the olive is cracked open, oil is released, and that liquid, touched by hands that are sheniyos, becomes a rishon, since this is the rule with liquids: they leap to the level of rishon. The liquid then turns straight back on the olive and renders it a sheni.
According to the Bartenura, this holds even where the olives are not terumah. Some commentators understand the case specifically as terumah olives, where the chain can continue further and the olives can be brought down to the level of a shelishi.
So the mishnah leaves us with two lessons at once: the purpose for which olives are set aside determines whether the liquid seeping from them prepares them for tumah, and a person's own unwashed hands can be enough to carry tumah into the food he is about to eat.