Sounds like your dad has a problem rather than yourself. Not being extrovert is a good thing, they can be a pain at times.
A small number of close true friends is far better than tens or hundreds of acquaintances who you simply know.
That said, being about to talk to folk is a good social skill. To expand yourself, it's sometimes good to deliberately tackle a thing you are uncomfortable with. Not so much as it stresses you out, but gradually until an uncomfortable situation becomes a familiar one that does faze you any more.
So, maybe join a club for something that interests you. Practice saying, "Hello" to folk there that you don't know, and maybe have a few irrelevant but generally interesting things you can talk about if needed. Most chat is unimportant anyway, it's the social interaction, getting to know someone, that's of value; and more importantly, being at ease with it because you've been there so many times it's no longer a worry.