Is it normal to purposely not get attached to people?

In my life people come and go, no one has ever stuck around. I start relationships knowing one day they will end, it makes the time I do have with them more precious since I know it won't be forever. I know people move, get busy, whatever and I tried so hard to keep the contact even if its only through fb but in the end they forget me and have passed out of my life. So iv lately kept a mental barrier that keeps me from getting attached to people, I still enjoy their company and treasure our memories but when their gone I don't get sad or miss them. I just think back and go 'good times, now onward to the next good times'. And when a relationship ends I don't really care or understand why the other person will get emotional, I'm like chill there's other people out there I ain't the only one. Maybe I'm just cold hearted now? But it makes life easier, I never get hurt or heartbroken.