The inability to compatibly resolve the two most important and basic theories (relativity and quantum throry) means we know either gravitation or quantum mechanics, or most likely both, are wrong, or at least incomplete, in the same way Newtonian mechanics was only partially right.

And that's been an embarrassment well-known for the last century. The word has a metaphorical use of the sore spot, that which sticks out, which is ugly, which is confusing or awkward. "This code is embarrassing" doesn't necessarily mean the author should literally feel embarrassment. It's just messy. (Yes, really. It's in the dictionary as a sense of the word.)