What does it mean when your father is afraid to tell other people you're gay?

I came out to my parents about 5–6 months ago. My mum was cool and said to me, after a few days’ being sad and frustrated, :“It’s okay, nothing has changed, we still love you.” My dad, who works for government and deals with a lot of people and lots of such “relationship” things, told me I could do anything I want but is still afraid to tell any other people about me being gay.
My dad really loved me. I can feel it, really. He cares about me a lot and would do anything good for me as long as he could.
It doesn’t mean that he’s ashamed of me, does it?
Should I just accept this fact and tell myself like “He’s not the god or the best person in the world.” and move on or something, or should I tell myself “Everyone just need a period of time to take it and I should be patient, maybe one day he’ll tell people around him ‘My son is gay.’ with no fear or sadness”?
I kind of don’t want to admit it but it really bothers me a little.