cat-and-dog life可不是说像猫和狗的生活，而是表示：“水火不容的，经常吵架的”，是个形容词。
首先，live/lead a +形容词+life,过着……的生活
I lead a happy life after marriage.
婚后我过着幸福的生活。
再看lead a cat-and-dog life就好理解多了：
形容夫妻间过着争吵不休， 水火不容的生活。
They finally divorced. They led a cat-and-dog life.
他们最终还是离婚了。他们之间水火不容。
The Blacks lead a cat-and-dog life. I hate living near them.
布莱克夫妇过着成天吵吵闹闹的生活，我讨厌做他们的邻居。
The whites lead a cat-and-dog life.
怀特一家过着吵架的生活。
Mr. and Mrs. Smith lead a cat-and-dog life.
史密斯夫妇过着成天吵吵闹闹的生活。
The couples lead a cat-and-dog life.
这对夫妻过着经常吵架的生活。
He and his wife lead a cat-and-dog life.
他和他的妻子过着吵吵闹闹的生活。
They led a cat-and-dog life, so they decided to separated temporarily.
他俩老是吵架，于是决定暂时分居。
Although they lead a cat-and-dog life, they always cared about each other.
尽管他们生活中偶尔吵吵闹闹，但他们依旧关心着对方。
They were so happy when they first started dating, but after 10 years together, they started leading a cat-and-dog life.
刚开始约会时，他们在一起很开心。但是十年之后，他们开始过上了争吵不休的生活。