My current PI is telling me that I am a very shy person and he is really pissed off, what I should do?

This answer will only focus on long term strategies that might help you avoid such situations as you move forward.

To succeed in academia you can't really seem to be shy and certainly not seen to be less of a contributor because of it. No matter how good your ideas are, if they don't get considered then you have very little impact.

However, that doesn't mean that you can't actually be shy, or introverted. Many successful scientists are very introverted and even some are quite far out on the autism spectrum. Shyness isn't a defect or a flaw, it is just a personal tendency. Introverted people, in fact, often are extremely productive as they gather internal strength from reflection, consideration, and thought.

But the trick is to learn to act as if you have a different set of preferences than you actually do. You can act like an extrovert naturally would even while remaining an introvert. You play a role in public situations that lets your thoughts and needs get notice in the deliberations and conversations.

But it is a skill that can be difficult to learn. I know, and I did it. The "face" that I show to the world has evolved over time. I once suffered from an "inability" to speak up when I should have and it cost me extra years in a doctoral program. But after that, I learned how to play the role so that my ideas weren't ignored by those with a bigger mouth.

In fact, you aren't limited by your shyness unless you let it overcome you. You can look people straight in the eye and explain your ideas to them. You don't need to defer to louder people.

One person, a friend, who is very prominent in the CS community and is a marvelous public speaker is naturally, and in person, extremely quiet and has some characteristics of autism. But he taught himself to do what needed to be done to have his ideas accepted and to act in public in a way that seems to others to be comfortable, even if it is not. One of his tricks was to join an acting group in which he learned how to "put on" a role and act within that role.

Some people just freeze when confronted. Other people explode into inappropriate behavior. Both of these need to be avoided. Practice is what you need to overcome them if you tend to do that. Preparation for meetings, with notes on what you might want to say can help.

Finally, let me note that people reading your several posts here probably don't think of you as a shy person. In your writing, you are able to say what you want to say. Some of that is the anonymity that the site affords. In a sense, you can hide the "real you" behind a certain invented persona. The trick is to learn to do that same thing in person. Invent a persona for yourself and act in the way it suggests, hiding your "real self". Yes, I do the same thing here as Buffy.

The situation is hard to evaluate without knowing exactly what the PI told you. I feel, however, that the problem here is not necessarely that you are a shy or timid person, but that you did not respect a unwritten social convention.

Today, in the lab we have a birthday, I had participated, but not so much as I feel anxious in the crowded areas. I felt very shy and that's is true, I withdraw from the party after 15 minutes and wished everyone the good.

Birthday parties or other celebrations are often moments where links between colleagues are created. In some cultures, leaving off after 15 minutes could be considered rude.

The PI ( head of the lab) informed I cannot assign two shy people to work together ( me and the prospective supervisor) as he thought we are going to fail to make a significant work.

This is a very strange thing to say to a prospective student, but, as research involves communication, the PI might fear that two extremely shy person could have problems with that essential part of research.

From your own account, you seem anxious in social events but you say that this is not a problem in professional event. You could ask for a meeting with the PI and simply explain that; ideally, you would provide proofs by the things you did that professional communication is not an issue.

However, I would suggest to be careful. If you found the PI rude now, you might want to find another lab.

It's one of the more disgusting facets of our society that Type B people want to be left alone, but Type A people are rabid in their efforts to change Type B's into Type A's. I don't like noise but I'm told that I "don't like to have fun." Something is wrong with me because I'd like to be able to talk to the person I'm with rather than have a band screaming in my ears all night. And they NEED to fix me. What I consider fun isn't. Only what they consider fun.

This bigotry is subtle, pervasive and devastating. If your shyness is the result of an emotional disorder, all the more crushing and ostracizing this is. And probably no place is it so concentrated as academia (as you can witness on this stack exchange daily.) "You play by our rules or you don't play at all." Type A's are bullies, and that's exactly what this PI is doing. Either be just like him, always agree with him or he throws a tantrum and somehow it's YOUR fault.

What to do? Say, "You're trying to bully the wrong person," and walk away. Repeat as needed.