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David Enoch has a fairly well known argument for moral objectivism that goes something like this:

Suppose we were going on a hike, and came across a lost puppy. And suppose that while I want to take the puppy with us and try to find its owner, you want to torture and kill the puppy. We have entered into a deep and seemingly irresolvable disagreement. Now the question is: should I stand my ground and demand that you not torture the puppy, and even prevent you from torturing the puppy? Or should I opt for an impartial solution: maybe we torture and kill the puppy this time, and the next time we take care of it and find its owner.

The answer seems obvious, I should stand my ground.

But then notice how different this is from a case of disagreement over what we should do when the only relevant factors at play are preferences. If you want to go to the movies and I want to go play video games, I certainly should not stand my ground and demand that you do what I want to do. In this case I should seek out an impartial solution: maybe we go to the movies this time, and next time we will go play video games.

The subjectivist cannot accommodate these facts, because on subjectivism the moral factors are just matters of preference. On subjectivism the first case is like the second, and you should not stand your ground.

So simply put the argument might go like this:

1. On subjectivism, interpersonal disagreement arising out of moral issues are really just disagreements arising out of differing preferences
   
2. When interpersonal disagreement arises out of differing preferences, we should seek out an impartial solution and not stand our ground
   
3. Therefore, on subjectivism, whenever there is interpersonal disagreement arising out of moral issues, we should seek out an impartial solution and not stand our ground
   
4. But we should not seek out an impartial solution, and we should stand our ground when confronted with interpersonal disagreements arising out of moral issues
   
5. Therefore, subjectivism is false
   
   This is Enoch's book, which I don't actually recommend for the most part except for the single chapter where he fleshes out this argument: https://www.amazon.ca/Taking-Morality-Seriously-Defense-Realism/dp/0199683174.