Great points, everyone. Max, that's a great analysis of Angel. Contrary to what people often say about Angel on BtVS, I think Becoming I is a great character episode for him where we get a rather good insight into his personality. The first flashback is one of my favorites in the entire verse (even with DB's accent) and the first time we see Darla in all her glory. This episode, in addition to season 3's Amends, sets up Angel the Series very well.
We don't find out his human name this time - I think it is only first revealed in The Prodigal - but we already get a hint at his lifestyle, resentment against his father, and his family's social status: his father has expensive silverware but eats with his hands; therefore, he seems to be a well-off merchant, probably new money, with no family tradition or high status (which puts a bit of a different spin of Angel's [problematic for so many reasons] statement that he despised the noblewomen of his time; the noblewomen of his time must have felt similar about him and his family, even though he may have perhaps had a chance to marry some impoverished ones, who would've nevertheless seen it as a step down). (Note: I'm not saying that the writers had a consistent background planned for him from the beginning or at least middle of the season 2, or that they had given it much thought while writing Halloween; they even changed his year of birth by a couple of decades). It is also indicated that Liam hates work (and presumably his father's work ethic) but wants to see the world and to be more cultured, at least in the sense of imitating the higher classes manners (and we see that vampire Angel enjoys collecting beautiful things and has a very tastefully arranged apartment; though it is amusing to think how he managed to come by all those things - stealing seems like the obvious answer).
We will later, in AtS, learn about his resentment of his father's religious views; Spin the Bottle shows a younger, teenage Liam who had a lot of Catholic guilt and was scared of going to hell due to his father's warnings. In that context, his speech to Drusilla as the priest in the (also brilliant) second flashback sounds like it could be reflective of the things he struggled with as a human. His words to his father, when he came as a vampire to kill him, were the sarcastic "here, Father, I have finally made something of myself". His darkly ironic adoption of the nickname "Angel" (because his beloved little sister thought he was one when he came to kill her) and his enjoyment in corrupting a highly religious, god-fearing and innocent girl like Drusilla - and making her a vampire after she had become a nun! - also add a lot to the picture of Angel's relationship with religion.
But it was not. Xander was not being rational or pragmatic there. It's not like they had Angel caged up in the library or tied up in the basement and were just discussing what to do with him. Angel was on the loose, soulless, evil and killing people, and there was no guarantee that Buffy would succeed in taking him out; there's never a guarantee, no matter how great a fighter she is. (She is the Slayer, yes, but if Slayers were guaranteed to kill every vampire they go after, they wouldn't all be dying so young.) Cursing him again would mean they gain another ally against Drusilla, Spike and other vampires, or at least (if Angel is too screwed up mentally after having his soul returned), take out a dangerous enemy without even have to risk their lives and kill him, not to mention that he doesn't kill all the people he's going to continue killing while he's soulless. Refusing to curse him and make him souled again just because you're scared that he would get away with his previous crimes, is not rational or pragmatic at all; it's putting revenge and hatred/anger/resentment against the guy above the pragmatic need to stop him ASAP. The one problem I have with the episode is that nobody thinks of bringing up that point - though they do make it after they know about Acathla. Yes, that's a much bigger threat, but it's not like Angel continuing to kill people and a possibility to make him stop means nothing? I agree with Vampmogs' and Sosa's views on the matter, Xander was just as emotionally compromised as Buffy, only in the opposite direction.
I do think he was more rational when he made his decision to lie to Buffy in part 2, but his decision was still strongly influenced by his dislike and resentment of Angel, just as Willow's determination to resoul him was influenced by the desire to bring him back and make Buffy happy. This is something that I'll talk about in my review when we come to the Lie.
Review of Becoming, part 2 will be posted a little later today/tonight.