What do Buddhists say about illogical self sacrifice?
Here are three possible angles to look at it from:


A genuinely selfless action can be a wholesome act of generosity and compassion. But...
A sacrifice of any kind can be wholesome or unwholesome depending on the deep motivation. If the action is meant to manipulate or punish others (or even yourself), it will have bad results. Sometimes we are not aware of how we can have selfish motives for apparently selfless acts, so we have to be careful.  
One of the "fetters" that binds a being to endless rounds of rebirths is attachment to "rites and rituals". So fasting as an attempt to propitiate fate or karma or God, or to achieve some kind of magical outcome, is useless. Prior to his enlightenment, the Buddha spent years starving himself thinking that that was the route to liberation from suffering. His motivation was pure, but he realized that it was pointless to destroy his body.