Nowadays Raising pets such as dogs and cats in big cities is

句子的主语是 raising pets such as dogs and cats in big cities 整个分词短语,当单数看,所以用了is.
pets such as dogs and cats 像猫狗这样的宠物,such as.经常跟着名词之后,表示列举
例如：There are few poets such as Keats and Shelly.像济慈和雪莱这样的诗人现在很少了.
Animals such as rabbits and deer continue to be active all winter,finding food wherever they can .像兔和鹿这样的动物整个冬天都是很活跃的,它们到处寻找食物.