Here’s a quote from the site you cherry picked

Some people may choose to go vegan, for some it may be because they do not believe in farmed animal practices and animal exploitation, for others it may be due to environmental concerns. Whatever the reason The Vegan Society is here to support everyone on their vegan journey.

Gee, looks like the vegan society also recognizes some people become vegan because of climate change… Or maybe you are going to redefine more terms so you can win your argument.