I borned...

I reach for a jar of marmelade.

On a compatibilist reading, I am unfree but not unnaturally coerced to perform this action. It springs from my every impulse, which springs from my ever-conditioning environment. I would not choose to eat the marmelade without my determined background, but, crucially for compatibilists, my marmelade would not be chosen to be eaten without me being the transeunt agent.

I emerge from my mother's womb and then enter a grave.

On a compatibilist reading, I am unfree but not unnaturally coerced to perform these actions. I would not undergo these changes apart from the determining factors behind them, but, as well, they would not occur except by me (qua transeunt agent).

Yet birth and death are not actions we perform, therefore compatibilism is false.

For,
if the conditions for a "free and rational" action, on compatibilism, are equally satisfied by my birth and death and by any choice (e.g. my choice of condiments),
but birth and death are not properly actions,
then compatibilism's account of actions is fatally flawed,
and compatibilism (qua theory of action) is defeated.