Thunberg spreads her message of emission reductions while travelling around the globe using carbon-intensive modes of transport and contributing further to the problem.
Greta flies all over the world to make her speeches, often travelling by jet, expanding her carbon footprint. This undermines her message encouraging the reduction of emissions and her endorsement of lifestyle changes to mitigate the impacts of climate change.
Greta travels by plane all over the world to address governments and international organisations. She eats foods that have been transported by plane, and she enjoys the luxuries in life that burning fossil fuels have afforded her. To speak out about a system that has afforded her many of the luxuries and privileges she enjoys on a daily basis smacks of hypocrisy. Even her publicity stunt which saw her sail across the Atlantic to address the UN climate summit in New York was appalling for the environment. A crew had to be flown to her. Instead of transporting one girl across the Atlantic by plane, her publicity stunt involved moving several people and heavy equipment across the Atlantic to meet her and assist her in her voyage. Overall, the voyage was far more damaging to the environment than it would have been if she had just flown to New York on a plane.
Those trying to change society for the better, still have to live in that society. She cannot be reasonably expected to live in a cave by candlelight and be expected to mount a serious campaign to reduce our reliance on fossil fuels. She is vegan. She tries to avoid air travel, and she undertakes small, environmentally conscious tasks like planting trees when she can and driving in a Tesla. She is taking plenty of steps to minimize her climate impact. If we all lived a lifestyle in which we offset and reduced our ecological where possible, the world would be a better, safer place. In going after the messager rather than the message, and attacking Greta as a hypocrite, the climate change deniers are merely demonstrating the validity of her arguments. Instead of engaging with her message, they would rather attack her behaviour, appearance and mannerisms. This proves her argument of "listen to the scientists" is inscrutable and is a testament to the moral bankruptcy of the individuals who continue to deny the existence of climate change in the face of overwhelming scientific evidence. 
[P1] Greta flies on planes. [P2] Planes are not good for the environment. [P3] Her message is one of environmentalism. [P4] Therefore, she is a hypocrite.
[Rejecting P4] Those who wish to change society still have to function within it.