I want to be social but I dont want to be

This is actually quite a simple thing to reason out. And one that perhaps you should be more understanding about.
The two most common reasons a person may say such things...
1) introverted - introverts Are social people, they simply go about socialization in a different way. Shyness can often (but not always) come with introversion. So this person may want friends but not have experience or confidence to approach people casually. I am this way. What you treat as a nuisance or a pest, to me would be a struggle that I wish I could overcome and even frustrate me in my failure to do so.
Introversion is not a defect. It is a personality trait.
2) depression - depression has a way of making you feel isolated, all the time. For some getting out of bed may be difficult, let alone helping others or making friends. It may make someone latch on to another that they feel has stood out to them in some way.
And since depression is more than just controlling your thoughts, it doesn't go away easily. Or for some people, ever.

I would encourage you to not assume this person understands they're being inconvenient. Or to talk down so harshly on someone struggling to make friends. Just because it's an inconvenient thing for you doesn't mean you have to look down on them, because it probably is a compliment to you that they chose you. Instead of being upset with them why not look inward and ask yourself why you aren't more patient or understanding with them?
Sometimes that person that is a fly in the way of your oh so important life is a hurting or desperate person doing their best to reach out and is under the idea that you may be the type that cares. If you can't understand how that's a good thing then that saddens me.
It's a similar mindset to seeing a homeless, hungry person then going home and complaining about what a nuisance they are to your life.
No, they're simply struggling and in need. And if you're unwilling or incapable of helping that is no need to put them down for asking.

I havent put anyone down.
I have done all i can to suggest ways for them to make friends with others but they just seem they wont. They are not homeless or hungry at all, and have plenty of people around them, family, flatmates, workmates.
I have invited them to many things but they wont join.

That is the weird thing. I had a birthday get together, invited this person, my friends were there all the time, and still they said they couldnt see me! I said bring a friend of yours if you want.

Then they say they want to be sociable and join this artist group but asked if I join. But i am not interested in joining an artist group and said so cos I am not an artist. I said you can join yourself cos you are interested and it would be good for you. Oh no they cant be with others. Then why ask me?!

Introversion and depression have varying degree's and affect people differently. Because your experience doesn't line up perfectly with theirs doesn't mean it can't be rooted in the same places.
And if they have PTSD that changes Nothing of what i said. Changing the mental illness, yet the message is the same.

But i can see this is a dead end discussion. I tried.

You know what we ALL can do? We all could pray for this person and for you, dear Lan. You may not be able to help or fix, but the Holy Spirit can.

They did ring again at 9:35pm left a message where they just said they ringing to say how are you but why when its my bed time would I want to talk right then.
Should I then ring at 5:35 in the morning saying how are you back?

Anyway I am going no contact for a while cos I am so tired of having to explain simple things and them confusing me all the time with being doubleminded. Cos I really dont know what to say.

I havent really had to say to anyone WHAT DO YOU WANT. The last time I did that the person swore at me I was so shocked I very nearly called the police.

This reminds me of a student whos now left class and they were always harassing my classmate and annoying them by trying to copy her answers and sitting next to her and always talking. But then saying loudly they were too shy and awkward and needed help.

years ago, there was a man who was my neighbour's brother-in-law, who asked me out to dinner. Unfortunately, I accepted and after that I could not get him to leave me alone. He would show up at my doorstep un announced, call me and leave progressively angrier messages, and he would tell me I was his best friend, he was fired from his job and told me he needed me at this terrible time in his life. My cousin finally intervened on my behalf, and told him to leave me alone.
I was at the point that I was going to talk to the police. For years I would see him in the city, and I always got nervous that he would see me too.

I know your situation is not exactly like mine, but, sometimes people's behaviour can be very disconcerting. I am 60 years old, and I have a lot of physical health issues, and I am learning to avoid situations and people that literally make me ill. I believe that, even as a Christian, I have the right to allow or not allow someone into my life.

Yep cos they annoying and ring at inapporpriate times. And I dont use my phone for that. I did say that, cos it costs me to txt and if its not that important and they want to have a screeds long conversation I cant really answer.

Yea, I am wary. I just said, if you want to be sociable, go help a neighbour. Or if they want to join a group but feels awkward for first time, ask one of the members to see if any can carpool with you.

They then said they would rather know a few people than many not at all. Im tired of explaining how, you can make friends with other people and dont have to know every single person. But if you dont go to meet new people, you wont ever get to know them.

What do you say to someone who confuses you like this.
They say they want friends but then make no effort to make friends. Or they only want to be your friend and nobody elses.
Or people that say your my only friend.

I feel very uncomfortable around people that do this.

Why would you announce to someone that they are the ONLY friend they have. This does not make me feel special. It makes me feel weird. Why me?

I