Me and my DH started having pets 25 years ago. (We have had cats and rabbits.) We've been through three cats and two rabbits. We have one cat left. She's 16 and a half. When this one's gone, we will definitely not be having any more pets and we're only around 50 years old.
The fact is, vet bills are WAY more high than they were when we first started having pets (and when my parents first had them some 30 to 50 years ago.) And that is taking into account inflation too. The costs are easily three times more than they used to be.
And don't anybody bother saying, 'oh, they've got so much better technology now and much more outgoings...' because 30 to 35 years ago they had better technology than they did 30 to 35 years before that. And big outgoings then too.
As quite a few people have said - insurance is sometimes pointless because you have to pay an absolute fortune for the ones with a good payout - like £10,000+.. More than many can afford. AND there are some things they don't pay out for, like treatment for teeth, and eyes, and long term conditions like diabetes and epilepsy.
If our cat started needing lots of treatment, and the vet said we will be paying 6 to 8 thousand £££, we would make the decision to PTS. She is around 83 in human years and we have given her almost 17 years of love - and a great life .. Would NOT put her through medical treatment and procedures to try and prolong her life by a year! And put us in the poor house at the same time!
Also YABU @Allelbowsandtoes because many people CAN afford their pets when they have them, and their financial situation changes and they struggle to afford the vet bills. So YABVVVU... 
It used to be a normal thing for working class people/people not on high incomes, to have a pet some decades ago... Now it's an absolute luxury. Like going to the pub, or a football match, or a UK holiday in a caravan... Used to be for the working classes.. now you need loads of money. These are all for people with lots of surplus cash now!