I remember my mum telling me how she had my hearing checked when I was about 3. The doctor said that I didn't have a hearing problem. I was just ignoring her Your son sounds very like mine was at that age, although mine actually has severe emotional, behavioural difficulties (EBD). Always remember, children are not naughty. They do things which are inappropriate but they are not naughty. I constantly have to say to my son, "I love you, but I don't like some of the things you do". There is a big difference.
The point is there is always a reason for what they do. Certainly it can be about pushing boundaries; finding their feet in the world and trying to assert some kind of authority. It's also why little kids love the bad guys in movies and cartoons. It's about power, which is something they don't have. At about this age they also go through the "you can't make me, I'm in control and I decide what I do" phase. Sadly my son's never grown out of this, but emotional development delay is part of his EBD issues
Anyway, sorry for the lecture. As others have said, it could be a reaction to something he's injested. For instance, my son is severely sensitive to all chemicals in food but also to straightforward sugar. But his biggest food sensitivity is a very common one. It's not azo dyes or aspartame or msg (although a a small amount of something like sugar free Fruit Shoot will make him climb the walls for half a day). It's soya. Sensitivity to soya causes hyperactivity, agressive behaviour and so on. And soya is in one heck of a lot of stuff, and things you wouldn't think of. Because it's cheap, it's used as a vegetable oil everywhere, even in organic foods. It's in sweets, in milk chocolate (soya lecithin), in foods. And the labelling laws only say that the manufacturers have to put "vegetable oil" on the label, not the source of the oil.
So I'd suggest looking at his diet very carefully. Cut out everything you don't cook yourself from scratch and don't give him anything that just says
vegetable oil on the label. It's a faff when you're shopping, but it might just pay off. Then again, the terrible twos last longer than two, and then you're into the "teenage threes". Like the terrible twos but with an opinion on everything
Good luck