These days we are incubating from late Winter through to late Spring/early Summer depending on how things go.
The reality is that you can hatch all year round with a good incubator in a climate where the temperature doesn't get too high. Incubators can raise the temperature but most can't lower it. If the outside temperature goes over incubating temperature you can have problems unless you can keep your incubator in a cooler room. In a house environment where you can keep the temp down, you can incubate all year.
Most exhibitors would choose not to breed in certain times of the year though because the climate during the rearing period matters a lot for growing out an optimum bird. Hot weather can affect appetite (birds eat less), it can affect their growth rate etc. Here in a humid environment we don't want hundreds of young chicks during the summer storm season because we know we'll have to deal with coccidiosis at a higher level and other diseases go through more easily. We want established youngsters and lower numbers by the time the weather is really hot and really wet.
Everyone's going to have a different opinion on this because they breed for different reasons and in different climates.
In the old days folk wisdom was that you should aim to get your pullets laying before Easter and then they would lay through Winter. There's a grain of truth in that. If you are producing layers you might time your hatches differently than if you are breeding exhibition birds. In the old days people who were hatching layers didn't want to be feeding unproductive birds through the Winter for months waitiing for them to come into lay. These days commercial producers control the environment eg. day length/light and those issues are less important.
There's always people hatching and selling chicks and there's always people who will buy them. Then they will come on here and ask us why their 20 week old pullets aren't laying in the middle of Winter.