The answer to this question is actually straightforward. Because of circumstance and because the Near Eastern wildcat can be domesticated, it was domesticated about 10,000 years ago. The Near Eastern wildcat (aka North African wildcat) is quite a small animal. In fact, as expected, it is of a similar size to the domestic cat. It looks a bit like a tabby cat although lankier. That, therefore, is why the domestic cat is relatively small.
The domestic dog is a domesticated grey wolf. The grey wolf is quite a lot bigger than the Near Eastern wildcat. This is why domestic dogs are generally larger and stronger than domestic cats.
Of course, there are many sizes and shapes of domestic dog because they been domesticated for up to 30,000 years so through selective breeding breeders have created a whole range of sizes. Some dogs are smaller than domestic cats. But, as mentioned, in general and on average the domestic dog is larger and stronger than the domestic cat.
To recap, the reason is that the starting point, the wild animal which was domesticated in respect of cats and dogs were different in size. In fact they were substantially different in size.
The fact that the big cats like lions and tigers are stronger than big dogs and wolves is irrelevant to this discussion. The important point is which animal was domesticated and therefore what is the starting point.
For the sake of absolute clarity and completeness, a male grey wolf weighs between 30 and 80 kg while a male African wildcat weighs between 5 and 8 kg. At the top end you can see that the wolf is 10 times heavier than the cat. That I think pretty well sums up and explains the answer to the question.
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