Philosopher Gonzago Rodriguez-Pereyra defines the very old and well-known "Problem of Universals" thusly:
But what then is the Problem of Universals? As I said, it is usually taken to be the problem of accounting for how different particulars can have the same properties.
And the australian metaphysician David Armstrong does it in exactly the same way:
[The Problem of Universals is] the problem of how numerically different particulars can nevertheless be identical in nature, all be of the same "type".
To me, for two particulars a and b to have the same property F, or be of the same type F, simply means that "a is F and b is F*. But I don't see why the fact that "a is F and b is F" is puzzling at all. Why does the fact that "a is F" and "b is F" need to be accounted for?
I really don't see any kind of incompatibility, while for Armstrong the fact that both propositions are true is, prima facie, a good reason to postulate the existence of a rather bizarre kind of entities (namely, Universals). In fact, he writes
I would wish to start by saying that many different particulars can all have what appears to be the same nature and draw the conclusion that, as a result, there is a prima facie case for postulating universals.
Moreover, he calls the belief, held by philosophers like Quine, that the Problem is not really a problem, and that it is a fact that does not require further explanation, 'Ostrich nominalism'. This is because, according to him, dismissing this as a problem means refusing to solve it, like an ostrich would do by sticking its head in the sand.
However, I still can't manage to see why a is F and b is F both being true is problematic at all. Could you perhaps enlighten me? I've tried by reading books and practically all the SEP/IEP articles on the subject, but these mainly address the solutions, which are hard to understand to someone, like me, who hasn't even got what the problem is all about.