Generally speaking, cats like the company of other cats. But, cats are territorial animals and that is often the reason for a fight. Sometimes if cats are bored and if they roam around free, they will often bring their new cat friend home.
Introducing a second cat to the home is always awkward. Cats perceive your home as their own territory. Your cat marked this territory with their scents. Litter box, their secret hideaway, toys, their treasures, everything and everyone (including you) is marked with their scent. This makes everything and everyone in your home their ownership.
So, the newcomer is always in an awkward position: new territory, new scents, and new rules. The resident cat who already “claimed” the territory will be the one who dictates the rules to the newcomer: where to lay down, when to eat, how much to drink, and where to walk. The “owner” of the territory will try to dictate all this to the newcomer.
Some cats love the company of other cats so much that they will be very pleased to get a company. However, they will not show their satisfaction at first. When they first meet, there will be hissing and growling. The resident cat will be jealous. It is not easy for them seeing you petting a newcomer. They are selfish, just like us.
When bringing a new cat to your home it is important, for starters, to secure a separate (so called “sanctuary”) space just for newcomer. Even a bathroom can serve as a temporary “sanctuary.” Prepare a comfortable bed, litter box, food, water and few toys and limit their movement around the house in the beginning because chances are that newcomer cat will try to hide somewhere where you will not be able to find it or reach it. This is because newcomer cat is scared and changing the living space is one of the most stressful events for cats. It is for us, too, but we will not try to hide under the wardrobe after moving to a new apartment. Or will we?
Another good idea is also to bring some cat stuff from an old home, like some toy or food bowl or maybe a pillow. You can bring this at your home before introducing a new cat. That way, your resident cat will be better prepared for the newcomer.
Anyways, now that you secured a separate space for the newcomer, you may allow the resident cat to peek into it, but don’t let them enter at least for the first few days. It might take some time for them to adapt to each other. In time, you will let them share the same toys and eat at the same time.
Sooner or later, you will witness a fight. It may even look as a serious fight where they will try (sometimes even succeed) to scratch or bite each other. But don’t worry, they will not seriously hurt each other. Consider it a final phase of introduction as they need to determine who the dominant cat is in order to continue living together.
Their hostile behaviour might take a while, even a week or two, sometimes more, but sooner or later they will start to get along with each other because, as we said before, ultimately, cats love a company of their own kind. Just give them time.