The first sentence was an overexagerration, but I have had near-death experience for my kid, and that makes you reconsider various things in life seriously. I am certainly not a violent person whatsoever, but from that incident I understood that I would disregard almost everything if stakes were that high once more.
But, coming back to the original issue - it all comes down to two different theories of ethics, opinions about what is good and just: in essence, if some choice equals to murdering one to save ten others [a simplification for the sake of argument, assume that no alternatives exist] , would doing so be good or evil?
There are valid arguments to say that doing so would be evil by the nature of the act.
There are valid arguments to say that not doing so would be evil, by the result of the act (10 others dying instead of 1).
And I do value a human life of "a racial slur of choice" more than a hundred sheep - archaic laws did value human lives in a couple dozen of domestic animals, and that whas when a peasant's life was considered cheap; we can and should be better than that.
And I do value my kids life more than your life - that is also quite natural, I doubt that you'd find any parents who think otherwise.
It all adds up. I mean, if you start discussing life and death, then most solutions aren't pretty; and discussing only 'pure' solutions means not saving (= murdering) lives - such as the lives of people that could have been saved by some sheep.