Understanding why cat fights. Wild cats have a strong relationship with their family. But when the cat wanders off on its own the cat tends to be more solitary.
If another cat crosses into their territory the cat is usually stand offish. This can happen with outdoor and indoor cats protecting what they consider to be their area, toys or a human. One cat will leave the room when the other cat enters and the more submissive cat may hide to avoid confrontation. Sometimes personalities just don't mix. Cats have different personalities.
To stop cats from fighting. Use a large piece of cardboard between the cats this creates a gentle barrier between the two cats. If the cats are locked together, pick one up by the scruff, which will force the release of the other cat. It is hard to correct the relationship when the fights are long. Separate the cats and let them cool down.
How to help the cats like each other. Have lots of patience and be very consistent.
Have the cats share the scents, by feeding the cats at the same time on the opposite sides of the door. This allows them to associate the others smell with something pleasant like wet food and treats. Be sure you spend time with each cat in their areas. Continue to swap their scent by mixing their used litter together, take a wash cloth and wipe down one cat's paws and tail and other let cat smell it, switching the cat's space.
Now you can let them meet face to face by putting up a gate or screen between them. This setup allows them to see and smell each other and they are protected by the barrier between them. You can remove the barrier completely once they get to the point to where they can see each other without getting into a fight. Have someone help you with this step.
When you bring the cats into the same room give the lots of attention and praise.
Be sure that the cats have their own litter box, food and water bowl.
Some cats may never get along. Hopefully, they can get to the point where they will tolerate each other.
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