Say 10% of the calories produced for me at a human go to waste. And I can convert them at 25% efficiency to usable calories via a chicken. Then I have just increased the yield of usable calories by 2.5%. In consequence, I need to buy less and thus emissions can be reduced.
And wheat can be converted to pasta, which can be stored for years, and can be easily made edible by brief cooking. You can reduce wastage of wheat to negligible levels, and chicken farming has non-zero overhead, so it seems unlikely that the chickens are an efficiency win if you take reasonable care.
You're not taking into account that, by virtue of being an animal taking in oxygen and creating carbon dioxide / other pollutants, the chicken itself is contributing to greenhouse gas emissions.
The question is, in real life, are the bonus calories we get from animal farming efficient enough so as to be worth those greenhouse gases? Given the massive GHG emissions of animal agriculture, it doesn't seem so.
Perhaps I'm misunderstanding your example, though: feedback appreciated
If you feed the goat 100 calories, there is no way you get back 100 calories.
It's always better plant and eat the food directly than to feed it to an animal.
Of course, if you're in a scenario where you live on a small island with no connection to the outside world, and you only have marginal land, yes, you need might need to have livestock to survive. But that's not what we're talking about here.