You are absolute right on the issue. It is a culture thing. You are thinking this the American way and thinking the military is an opposite and separate entities from the administrative government. In that perspective, Hu is being one upped by the military. In Chinese culture, however, the military branch is a subordinate entity instead of an opposite. The father doesn't get embarrassed if his child obtains a great achievement.
One of the really strange thing from Epoch times' argument and the article you linked is the claim that J-20 is embarrassment because it "hinders improvement in relationship between US and China". How did they come up with that one and expect anyone (perhaps aside from an American) to swallow it? Your country being able to level the technological playing field on one of the most vital area of military technology is embarrassing? Let me put it bluntly. The J-20 gives Hu an enormous bargaining chip in the negotiation table and give him a huge advantage in the negotiation position. It is even simpler to understand why he arranged it at the specific time, but claim to not have prior knowledge. He did it so Gates and other visiting delegates will not have time to prepare a response. Basically, surprise the opponent and hit them because they can organize a response. It doesn't get any simpler than that.
As you say, it's not the test itself that is problematic, but the timing. The US is under no pretense that China does not have the right to build up its own military forces.
Beyond that, I understand what you're saying, but such a "surprise strategy" only works if the counter-party interprets it the way you want it to. The US didn't translate the events that transpired as some kind of "
gotcha! what do you think of them apples?!?" sort of situation. The US instead interpreted the event as showing an out of control military functioning with a free hand, and without the prior consultation of its nominal superiors, the politicians.
To use your analogy, a father invites his rival to dinner to try and alleviate the tension that has long existed between them. The son suddenly shows up waving a gun around and winking at the rival. I guess the father can be proud of his son for having a nice gun, but meanwhile, the son has completely undermined the father's attempts to improve the strategic environment.
Fast forward to today. If such thinking still holds, then the US cannot trust any calming words coming from the political leadership in China ("peaceful rise," etc.), because the military is not under the firm control of the political echelon under these optics. Now the US is pivoting to Asia because it doesn't necessarily believe that normal diplomatic relations will ensure peace and stability in Asia. That is, the US may establish understandings with the Chinese political echelon, but what does it matter if the Chinese military is allowed to do whatever it likes?
From an American perspective, that's a tremendous failure for the Chinese political echelon. I guess for the Chinese political echelon, they can be proud of ensuring that no one understands what they're after, which has the advantage of ensuring surprise, but the disadvantage of guaranteeing mistrust.
In any case, that was all under Hu. Xi supposedly has consolidated military control within his hands, so we will see if he can re-establish the idea that when he makes decisions, they are followed by the military.
Well yes, according to the US defence secretary, President Hu "seemed" to have been caught unaware by the test.
But that is a really subjective thing, who knows what was really going on there, and whether the US defence secretary was right in his perception or not, and whether that was intended or not. Or whether some other funny games were going on behind the scenes. And why did Robert Gates make such a big deal out of something so subjective?
The one thing we can say is that Xi Jinping seems to have consolidated his power base much better than Hu did.
In Great Power politics, perceptions matter (as I detailed above in my reply to Tranquilium). Even if it were not intended to be portrayed that way, the J-20 test did no favors for Hu.