You are right that there is a valid and striking difference between modern art and renaissance/gothic art. But unless you give us your own objective definition of art and argue as to how it follows logically, your argument is useless.
I don't like modern art, either, of course. There are plenty of kinds of "valid self-expression" that I would rather never see, and modern art is a good example. But if art is just self-expression, than it cannot be argued that modern art is indeed art. And I agree with Clo that art is subjective and that people see beauty in the oddest of places. Although I strongly disagree that there is much good in modern art.
If I were to bother explaining why I despise modern art, I might begin with an argument to support my superior definition of art. Because, like I said before, if it is simply self-expression, it is no use saying anything more than, "Wow, I think this is pretty but I think that's not". But even if you don't re-define art, you could probably be more articulate in the expression of why you think modern art is useless. I think the lack of skill that it requires is a good point, but there are more. I'm sure you can find them.
Purpose. Think about the purpose of the modern artists versus the purpose of your darling renaissance guys. I love them too.
Cheers! Good luck with this.
