@NogShine The central tenet of the form of veganism conceptualised in the UK ~70 years ago by a small group of people, which I think has become quite widespread here, is not to use animals. Are you familiar with the philosophy of Kant?
The idea that animals should have something like what is called bodily autonomy in relation to humans in other theories is a sort-of connected belief... personally, I believe in bodily autonomy and so I wouldn't keep a pet at all (I'm also a clean freak - I think it's totally weird and gross to keep animals in the house walking all over the place)
but others think that keeping a pet isn't a violation of their philosophy of veganism, or they keep rescued animals as part of their family
but they still worry about the sources of meat
Meat comes from farmed animals... in the UK, many vegans actively campaign to shut down livestock farms, rescue mistreated farmed animals etc, as well as encouraging others to give up meat
by buying meat for cats and dogs to eat, we are supporting the violent/abusive/animal-using farming industry
but kept animals can't make a choice about what they eat - they accept food from us, or hunt for themselves... I think it would be violent to force anyone to follow a particular diet... I think coercion violates the principles of non-violence and bodily autonomy that I believe in. So the tension between the rights of the home-kept animal (pet) and the rights of the farmed animal (livestock) for me is a difficulty in vegan thought. The easiest conclusion is that it's wrong to keep pets.