In the case of beef, the planet can’t sustain the rainforests being chopped down for gazing land and the methane production.
I should point out that virtually all beef cattle reared in the UK - and in the US - mostly consume food inedible to humans. They up-cycle grass into top-quality protein, they eat brewers grains, they eat the husks and stalks left over from various forms of grain production.
Methane, it is true, is a potent greenhouse gas, but it cycles through the system very quickly. It's also worth bearing in mind that there have always been large numbers of large ruminants producing methane, and that much of the methane currently released is from rice production and also from degraded peat (e.g. the Fens, which produce a lot of vegetables). Nothing changes the fact that the climate crisis is mostly there result of burning fossil fuels.
No we do NOT own animals. The fact any animal exists, as a species, means it has as much right to exist as any human.
That is an ethical belief, not a statement of fact. I don't think I own the wild animals that choose to hang out in my garden. I do own my dogs. I take responsibility for them precisely because I own them. The days in the UK of the local dogs wandering around the streets all day, and possibly changing the house they returned to at night because they felt like it, are long gone.
Besides, where do you draw the line on the right to exist? Headlice? Fleas? Ticks? Rats? The flock of 200 wood pigeons that descends on the pea crop? If we didn't kill animals - either directly by culling them before they eat everything we've been trying to grow, or indirectly by completely depriving them of habitat by sealing it all up in polytunnels or producing it in vats in large factories that use up a substantial acreage - people would starve. It's one reason there is so much hunger in so many countries: the crop is lost not just due to droughts or floods or poor soils, but because it's eaten before harvest, or eaten after harvest, by vast numbers of insects, birds and mammals.
I suppose deciding that nobody must kill any animal, ever, anywhere, would rapidly solve the human over-population crisis, but you'd be indirectly killing billions of people if you did that.