Thing is Hully, you can both be right.
I know that sounds like I am impaled onthe fence but, whilst you are trying to save the cat, she clearly is playing out some need via the cat.
And if you ever want to see full on defensive irrationality at play just question someone about their drinking, over spending, cat fattening....whatever their crutch of choice may be.
I don't want to criticise your friend because she is your friend - she must be nice. So there must be something in the situation that upset both of you iyswim.
I love you Hully but you can't save the world. Sometimes you have to watch quietly until there is a moment to help and support. People don't want to be faced with honesty sometimes, even if delivered with love. People don't accept open honest advice easily. They have to be annoyed, go away, think about it, acknowledge its truth and grudgingly accept.
Have you learnt nothing from AIBU
You are also immensely comfortable in your own skin. Lots of other people get more defensive and prickly as they age, not less so.
You are smart and honest and like directness. Others can't take it. They need flannel and time to figure things out.
I am so sorry you feel sad about this. But please don't change or despair. It isn't a choice between 'say everything' or 'say nothing'
Sometimes i think you just need to wait a beat or two.