Okay, deep breath. Maybe point out that of course farmers are vital to the prosperity of this fine country — no farmers, no food. But it´s not a question of supporting or not supporting, as much as it is a question of securing the survival of the human race. If we plan to inhabit this planet in the future we need to eat, and drink, a lot differently from here on in. Perhaps your dad has heard of World Overshoot Day? If not, it might be worth a family google. And as you have probably heard, but maybe your dad hasn’t: Producing plant-based food is a significantly more resource-efficient way to put food on the table.* Lastly, you could play the ‘Top Scientists Card’ like, “Top scientists from the UK government’s official advisers (the Committee on Climate Change) say that people should cut the amount of meat and dairy they eat by 20% to combat climate change** starting now.” Mic drop. Or whatever it is the kids are saying.
*Scarborough, P. et al (2014) Dietary greenhouse gas emissions of meat-eaters, fish-eaters, vegetarians and vegans in the UK
**Committee on Climate Change (2020) Land use: Policies for a Net Zero UK https://www.theccc.org.uk/wp-content/uploads/2020/01/Land-use-Policies-for-a-Net-Zero-UK.pdf