I have 5 kids (20, 18, 10, 8, 6) and none of them ever threw a tantrum. we had some arguments, and they would sometimes cry after a decision had been made, but they never tantrummed.
therefore, I disagree that tantrums are normal.
it is my belief that by the time a child gets to the age of the so=called 'terrible 2s', that they have already cultivated tantrum behaviour and it is a solid part of their personality. in other words, a tantrum doesn't just pop out like rain, it grows over time. like an oak tree. and by 2-3, you're looking at a down=line behaviour with foundation, not individual occurrences of somewhat related bad behaviour. To put it more harshly, if your 2yo is throwing tantrums, blame yourself for a year or two of what could have been better parenting... more on this later.
at 2-3, it's not too late to put the kibosh on it. but it will certainly take some harsh changes and will definitely take time, effort, patience. because at it's core, it's about control. who controls the relationship. "I'm the parent, I make the decisions, you will like it and you will sit your ass there until i say you can get up." or whatever... (yeah cussing refer to How do my wife and I stop our son from learning to swear from us?)
Understand: a child this age only knows what they want and they do not understand subtlety. negotiating will only result in you giving in and not getting anything. even giving in a little "ok 5 more minutes before bed" is still giving in. so be hardcore. "can i have 5 more minutes?" "No."
Now some parents can do this. what they can't do is maintain control. it's the hard part and can be done without spanking. in the above scenario, when you make them sit down, you have to be in control, make them sit and stop the noise. it will be trying, they won't like it and they'll fight you the entire way, but you're bigger and you absolutely can be in control of the relationship...
and here's why you want control: it is much easier to define the boundaries of the real world from the INSIDE than it is from the OUTSIDE. in other words, you'll be more successful in releasing them to reality a little at a time than trying to pull them back in a little at a time. if you control every aspect of their life today, and over time give them more and more freedom as you think they're ready... just a little bit here and there to give them their control of their own world, then they will have a much tighter foundation as they get older.
as far as the taking the blame goes, it's another way of saying that you've identified the problem and you admit to it. every 12 step program starts with admitting and accepting that you have a problem... because if you can admit to yourself that "i probably could have done better in the past" then you absolutely will do better in the future.
i look at my 20 an 18 yos, but even at these ages after i've long since stopped telling them what to do, they actively listen to me and accept my advice. they are proof positive to me that the way i'm raising my 6 year old may not be the nicest or the best, but it actually works.