I also get the impression (more so from fanon than canon) that Quentin actively despised Giles (partly because he'd rebelled and had his Eyghon phase and partly because Giles got to be an active watcher, while Quentin was stuck on the bureaucratic side of things); my belief is that Giles was assigned to an untrained slayer with the hopes that both would be killed and then the Council would have a new pair (one they hoped they could control closely). But, hey, just my imagination running wild!