First up it does seem like you are making progress, no matter how slow it seems.
Secondly it is probably worth really defining what you want your social life to be in order to be happy with it.
You said you wanted to 'go out' with people. What is the feeling that you want to gain from 'going out with people'?
An example underlying goal might be that you really desire to be able to have honest conversations with people that care about what you care about. Just an example.
There is another approach you can try, instead of trying to get people to, go out with people; try going out to meet people where other people go out to meet people.
So go to places and do things that you enjoy and are interested in that other people also participate in.
So if you love art, go hang out at an art gallery, like basketball? join a team.
It's not about making people like you. If you be yourself and enjoy being yourself then there will be other people who like to be around you.
Remember to that it is fine for you to initiate the 'going out', invite people to a new restaurant you want to try, invite people to your place.
Make it an experiment and try stuff out. If you fail there are a lot of people left to try
