Lets remember how this started. BAA, the owners of Heathrow want to expand their airport in order to create a hub. This would allow people from smaller airports around the UK and europe to fly into the airport and connect to a larger number of international flights. People are already doing this but via places like Amsterdam. It would also free up capacity on the main runways.
Somehow along the lines this was turned into a need for an extra runway being needed somewhere in the south east. This is like me asking for permission to extend my house as my family has grown and being told they will allow the guy across the road to do his instead.
Gatwick may or may not need a new runway. It would certainly like one as any airport would. It is a completely different matter however to the LHR plan. Gatwick knows that should LHR expansion go ahead they will likely not be granted permission to build one for decades and this is the reason they have started the whole Gatwick vs Heathrow debate.
Gatwick will never be allowed to grow into the hub that LHR wants to be so the debate should really be about whether or not the UK wants this hub and spoke approach. From speaking to my friends and family in the north I would say that once people realise that they will be able to go from their local airport to pretty much anywhere in the world with just a short flight and easy connection at LHR they change their mind from being totally disinterested in the third runway to being all in favour.
I would actually be quite happy for both LHR and LGW airports to build a new runway from a purely operational perspective. But unfortunately, there is no "give" about it. They will be extraordinarily expensive to deliver, particularly the LHR option. And I am very keen to ensure that the successful project is entirely privately funded, including all support works required to upgrade surrounding general infrastructure in consequence. And privately financed in a watertight manner such that the project cannot default back to taxpayer responsibility in the future due to some loose state-underwritten guarantee
Given the benefit to the UK from the above I really do not understand why you are so against any of the taxpayers money being used to finance at least the transport works. LHR is the UK's premier airport and brings in billions of pounds to the economy. To be against government investment just because it is in the south is just sour grapes. Look at the timescale. As has been said over and over the roads in that area are in need of upgrading now so a redevelopment would likely be done anyway.
Regarding the air pollution argument. We are talking about 10-15 years down the line when it will become operational. The A380's and dreamliners will be old aircraft by then. A newer era of aircraft and engines will be both quieter and greener compared to what we have now.
Trains cars and buses etc. will all be more efficient and less harmfull to the environment.
The hub and spoke arrangement will also mean less numbers of aircraft flying long haul out of the UK, less stacking of aircraft and less road/rail journeys to LHR and Man etc.