Cats are very independent but sometimes they can still get frightened.
The first thing you should do if you notice your cat is acting differently towards people, places or things is to take them to the vet. If your cat is in pain because of a condition or sickness they will be acting out and avoiding you and other guests because they don’t feel well. If your vet gives your cat a clean bill of health then you know it is just something your pet needs help with socially.
Cats that are fearful can show it in many different ways. Some cats will run and hide, some will eliminate their bowels, and some may even just stand there like a frozen statue. In any of these situations your reaction as a cat guardian is to pick them up and comfort them, this may possibly be the worst idea.
By picking your cat up you are showing them it is ok to be fearful. Instead let them go.
First start with figuring out what your cat is afraid of, if it is a person or thing then put that person or item on one side of them and you and your cat on the other side. If your cat seems comfortable still then slowly move closer to that object that scares them. Use positive reinforcement each time you move closer. Use treats to reward them and let them know it is ok. If your cat seems to tense up or seem like they may be getting afraid take a few steps back and start working forward again. This may take awhile but once your cat realizes the person on thing frightening them is not going to hurt them you will have a happier household and safe home for your cat.