It's more that their brain is only just beginning to process emotions. Up until now they've been pretty passive and their emotional state was quite immature, pretty much happiness and fear. Now they are starting to experience other feelings too, sadness, anger, frustration, confusion, they are starting to realise that they can communicate but may not be able to do so very effectively, they now understand that you are a separate person but still don't really get what that means so they think that you can read their mind and don't understand when you don't. They're starting to realise that there are a lot of different options which might be available rather than just the thing in front of them right now and that's confusing and overwhelming, they want the green plate, but no perhaps the red plate is better, they meant yellow but got the words mixed up, now it's all too much and they can't handle it.
Try not to think of tantrums as naughtiness but more of an overwhelming feeling. It is hard to hear "no" especially if you've said yes before and they don't understand that this time is different. It can help to explain, but don't go into long waffly explanations, just keep it short. Or do a "delayed yes" like "We can go to the park after lunch. Right now we're having breakfast and then we need to go to the post office".
They have hormone surges a bit like teenagers, they want to be independent but they don't really understand moderation so they try to be independent about everything. They're not that co-ordinated yet so things they want to do, they can't do and that's frustrating. Adults and older children can handle emotions better because we've experienced them a lot of times before and we can put them into context, but toddlers can't because they have a poor sense of time (at two, only "right now". By four you get "this day" and "before this day". They're about five and a half by the time they can really anticipate something in the future.) They can't imagine how they will feel later, which is why everything is "my favourite" or "I hate dis" (including mum + dad!) Anything bad is the worst thing ever, anything fun or good is the most hilarious thing ever.
Toddlers are awesome but you need to try and look at things from their point of view, or they are just frustrating and difficult.