Your argument basically is a professional motte and bailey fallacy.
And you cannot conclude objectivity by consensus. Physicists by consensus concluded that Newton was right, and absolute... until Einstein introduced relativity. You cannot do "proofs by feel". I argue that you DO need to answer the deep problems in mathematics to prove that 1+1=2, even if it feels objective- that's precisely why Principa Mathematica spent over 100 pages proving that.
In fact, I don't need to be a professional philosopher to counterargue a scenario where killing a baby for sport is morally good. Consider a scenario: an evil dictator, let's say Genghis Khan, captures your village and orders you to hunt and torture a baby for sport a la "The Most Dangerous Game". If you refuse, he kills your village. Is it ethical for you to hunt the baby for sport? Not so black and white now, is it? And it took me like 30 seconds to come up with that scenario, so I'm sure you can poke holes in it, but I think it clearly establishes that it's dangerous to make assumptions of black and whiteness from single conclusions.