The answer is: city centre traffic design. Yes, I am a bit of a zealot when it comes to traffic lights - I may sometimes join pedestrians when the little green man lights up, but otherwise I never go through red lights. The problem is that, once you reach the Cathedral, traffic lights multiply like rabbits on all main roads leading anywhere. This is compounded by the one-way system. I can't help but think that this is all design with the car in mind, with some provisions to appease pedestrians by providing them crossing points at frequent intervals (in the understanding that, at busy times, they will ignore all lights and just cross when and where they want to), and cyclists just do not feature in these calculations.
I have tried de-touring to side-streets. I have actually measured myself against other cyclists whom I knew were going to the same destination and stuck to the main roads, so I can say that side roads may give you the impression of saving you time, but in effect they make no difference at all - not with any consistency, at least. You see, it all hinges on how the gods of traffic lights look upon you: some mornings they show you nothing but green, other times they conspire to slow your progress to a miserable crawl. The former usually happens in sunny weather, the latter tends to coincide with rain (at least in my memories).
I could, of course, join the legion of cyclists that to their shame simply ignore traffic lights and treat busy crossings as challenges to their balance skills and hand-foot-eye coordination. But I just don't want to - the moral ground, once you get to it, is a very comforting place and I'd like to remain there and feel entitled to be sanctimonious when I want to.
More seriously - and I never thought I'd hear myself say this - the solution... is revolution: pedestrianise more of Manchester, off-set by a park-and-ride scheme (perhaps building on the successful and free Metroshuttle) and thus create the conditions for a network of pedestrian and cycling avenues into the heart of the city.
You may say I'm a dreamer...