Actually you can, but for that you need a logical proof. While the existence can be proved by exhibiting a case.
So you can’t prove that something does not exist, unless you make a proof of the absurd of such an existence.
Example I can affirm that cats “only black and only white at the same time” do not exist, because it is intrinsically absurd.
But then I can have lived my whole life without seeing a single hairless cat, does not mean that this is a proof that there are no hairless cats.
Here the issue is that DMC is affirming his opinion as truth, without a single argument for this. The “it’s obvious” argument is not one : it actually shows the impossibility to make such an argument.
The real matter here, is that many people can have different opinions, it means people who affirm arbitrary choices as truth are statistically more likely to be wrong and misleading people - that is, make people act based on wrong assertions.
DMC is just claiming something he does not like is responsible of all the issues in the game. Nothing more. Maybe I would do the same if I cared enough (about HS). Still I like Eve and as much as I wish him to enjoy it, being so self-centered IMO means he can’t have a constructed opinion on the topic.