The real reason people do not want to take their sick pet to the vet after hours is either due to laziness, on my gosh they might miss the hockey game, or due to the fact that they do not want to pay extra for emergency care.
Most veterinarians have an additional charge for calls made after hours. Big deal, this is your pet's life we may be talking about. The very least you can do is call, find out what the extra charge is, and decide if you can afford it.
You may even be able to talk to the veterinarian, explain the symptoms, and have them suggest if the pet should come in right away, or if it can wait until morning. You should know most will suggest bringing in the pet at the time, because depending what is wrong, waiting could threaten its chances for survival.
You should never wait if your pet has a fever of 2 degrees more than normal, if it is very young, very old, or pregnant and been straining to deliver for more than 1 hour. Black smelly diarrhea, can be a sign of parvo, this cannot wait. If your pet is unconscious you need to call a vet, also do not take the “wait and see” approach if it has swallowed poison. CALL THE VET!
Of course many after hour, especially weekend, veterinarian appointments can be avoided if you simply take it to the vet if symptoms first show up during regular open hours rather than hoping they go away on their own. There is nothing worse, and more frustrating to a vet, than a person who noticed their pet was sick on Wednesday but they waited until it was really sick on Saturday night before calling for help.
When you call a veterinarian after hours you either get their answering service, or may get the veterinarian themselves. Be respectful of them and their time, they do not want to drop what they are doing any more than you do, but it is their job. Do not argue about having to pay extra simply because they served you after hours. When was the last time you had a car mechanic look at your car at 2 in the morning?
Tips on When to Take a Sick Dog to the Vet
Tips on When to Take a Sick Cat to the Vet
Your pet is your responsibility, when it is ill, no matter what day or time, you need to suck it up and... well... deal with it.