Just to expand on this a little for the benefit of the OP...
Producing an evidence pack is a specialist job, it requires a considerable investment of time (and therefore money) on the council's part by someone who knows the fine points of all rules intimately. This means that it's the first point in the process where the council risks anything much more than the price of sending a couple of letters. They make you play 'double-or-quit' with the discount, making them produce an evidence pack is point where they have to up the stakes on their side. We often see councils fold at this point, which they do by presenting no evidence. This is one good reason to let them go first... you would be wasting your time assembling your evidence if they don't present anything.
Sometimes they fold because it's the first time anyone who understands some of the more technical challenges to PCNs will ever look at what you have been saying which means it's also the first time the council know they will lose at adjudication. Some more cynical councils play a numbers game, they know a lot of people will fold at the NTO stage, so they go that far even in cases where they don't have a leg to stand on. Occasionally they fold because they lack the resources to produce decent evidence packs, Barking and Dagenham seemed to go through a phase of not being able to produce evidence packs at all for several months last year. So another reason to let them go first is that they might not bother.
Another reason is to maximise their workload. If you go first and only have 1 or 2 lines of defence, they can do less work and concentrate purely on rebutting your points. If you make them go first they have to cover all possibilities, which they probably won't do so well. Because councils are weighing up the cost of carrying on against the chances of winning, they have to wager a bit more (non-reclaimable) effort and are therefore more likely to fold when they know they will lose.
This leads to another reason: some defects in council documentation only come to light at this stage. We sometimes see councils folding for no readily understandable reason. Given the fact that we quite often find defective (or missing) TMOs and TMOs that don't match up to signage, it's reasonable to suspect that sometimes the council finds this sort of thing out in the process of producing evidence packs, and folds rather than having to admit they messed up.
Next, there's the old military adage that you should never interrupt your enemy when they are making a mistake. A lot of the time cases are won at tribunal not on anything to do with the alleged offence, but because the council has missed something essential out of the evidence pack, produced the wrong documents, or not understood that their documents are not up to scratch. So, this is another reason to let them go first: Allow them to shoot themselves in the foot.
Others could probably add to the list, but I hope that's enough to explain it.
