Is it normal to not want to socialize with people?
Mostly.Normal for most people
Yes, it’s normal to prefer your own company or have stretches when you don’t feel like socializing. It’s worth paying attention if avoiding people is a big change for you or is making you feel lonely or stuck.
Some people recharge around others; others recharge by being alone, and plenty of people fall somewhere in between. You don’t have to be outgoing or say yes to every invitation to be doing life correctly.
It may help to notice whether this is simply your usual preference or a recent change. If you want connection but feel unable to reach out, or isolation is making you unhappy or interfering with things you care about, consider talking it through with someone you trust.