Here's part one.
Miravalle's second argument is the "moral" argument. That is to say, we all appear to have innate moral convictions, but that those necessarily come from god.
He briefly props up a straw man of "we get morals through observation" but knocks it down with "but we see people do bad things, therefore we don't get our morals from the world around us". He doesn't, however, notice that this also knocks down his thesis, that our morals are innate. I've argued elsewhere that morals are innate, but not from god. To put it briefly: they've evolved as a mechanism to foster cooperation so that each of us benefits as the group benefits. Evil is, in this model, either an alternative approach (psychopathy as a method only feasible for a small minority of the population) or when two groups come into conflict (when morality is based upon defining an in-group, some people will necessarily be defined as out-group and not receive the benefits of moral cooperation).
He also tries to argue that morality can't be in some way naturally innate because it's not innately selfish. He differentiates personal preferences from morality (appropriate) but claims that an empathic drive cannot be in any way innate. This is wrong because it has been empirically shown that, except among psychopaths, empathy is innate; there's a whole chunk of brain that's given over to considering the needs and desires of others.
He argues that moral outrage is entirely separate and different from disappointment over unfulfilled desires. I believe the implication he's striving for is that our personal desires, being small and petty and selfish, evoke a small, petty response whereas our moral convictions are a larger striving for the numinous and evoke a larger response. The difference between finding out there aren't any cookies left is obviously different from the torture of a child, and it's obviously a difference of kind rather than degree, but it certainly doesn't imply that it's somehow an external, imposed response. Say I step out of my house, lock my door, and turn to see a dog ambling in circles with a hesitant, lopsided, shambling walk. I'm going to quietly freak out about the possibility of being attacked by a rabid dog and attempt to quickly, quietly get back inside. Contrast that with stepping barefoot in a pile of dog shit on my way to get the mail. The disgust and fear responses are as different from one another as they are from hunger or sexual desire, yet all are wholly natural. There is nothing in his argument that actually distinguishes moral outrage from a natural, biological impetus.
His third quick-counter (part of the structure of debates is to set up and knock down possible arguments by your opponent) is that morality is cultural. Cultural relativism is a favorite opponent of apologists, because they hate hate hate relativism. If morality is not absolute, how can it really be a thing? He specifically links it to progress (I believe he's being very smart there, playing to the audience, gathered by an atheist/agnostic organization), saying that progress is meaningless in the absence of an external absolute against which to measure it. He's entirely incorrect; there's no external metric against which to measure technology, and yet my cell phone is clearly a superior and more sophisticated device than ENIAC.
He thus claims to have eliminated all other possible sources of morality, and that the alternative is therefore god. He then proceeds to try and make the argument from logic.
Next, Part 2 Part ii.