cell cooperation

It wouldn't be called cooperation if that system itself didn't have contradictions like cells sacrificing themselves to clot blood, overriding their self interest to remain alive. Cells are also marked for death and if they break that system they can bring down the whole structure (cancer, auto immune disorders). Cells have to balance their self interests with their communal interests and that contradiction creates a higher level of organization than the simple parts (cooperation).

Another, more basic contradiction is requiring energy to be alive because living (action) requires energy, so we always need to be using energy to find energy (it takes energy to produce and consume food). If we don't get enough energy to sustain ourselves we waste away into death.

negative and positive ionic forces at cell membranes

pH stuff in biology

oxidation/reduction

absorbtion/excretion

male and female

lots of them

Inhale/exhale, activity/rest

Considering that the end state of the universe is, as far as we know, energy being so spread out that no reactions or anything could exist, I think our very universe is a contradiction.