It's not about the generation. Burning methane results in a 1:1 emission of CO2 [0]; literally the equivalent of just dumping pure carbon dioxide into the atmosphere.
https://www.quora.com/What-are-the-products-of-methane-burne...
But Musk needs this process to become economical so that Mars can become economical.
(The same tech may, ironically given Tesla, compete with batteries for the energy storage PV calls for).
Take CO2 from air => Turn it into methane => Put it into rocket => Burn it back into the air
The bad part with burning fossil fuels is that you are putting carbon in the form of CO2 into the air which was previously locked under ground in the form of coal/gas/oil. If you are burning carbon that you extracted from CO2 in the atmosphere, there is no such problem, assuming you didn't use fossil fuels to extract that carbon.
It's not that simple. What you're describing is free energy. We're still burning fossil fuels to extract the methane. Maybe that could be powered by renewables one day. But as of now, it is not.
https://www.sciencemag.org/news/2019/07/former-playwright-ai...
If you've got a problem with that I imagine your real issues are about status envy not environmentalism.
If SpaceX/energy company deploys a new nuclear power plant (and one day fusion) to provide the energy, why should you care? It's a new energy source and not competing away your personal idea of worthwhile energy use.
https://www.nextbigfuture.com/2019/12/spacex-rocket-emission...
In addition, methane combustion produces 2.75kg of CO2 per kg of fuel, while kerosene produces 3kg CO2 per kg of fuel. If they are able to fit 20% more passengers than a 747 due to the larger internal volume then they would be within about 66% efficiency on a CO2 emissions per passenger basis.