I've seen people talking/ranting/debating about this, I thought it was a nice subject, and so I decided to make an article about it. Here I go!
(I know, that was a terrible introduction.)
WARNING: If you haven't watched Frozen yet, I suggest that you don't read this if you don't enjoy spoilers. But if you do, well, it's your choice. Don't say you weren't warned.
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At the first part of the movie, Elsa and Anna were playing in the middle of the night. An accident caused Anna to be hit by Elsa's powers, and so Elsa called for her mother and father. They went to the trolls to find a way to cure Anna. Grand Pabbie, the leader of the trolls, cured Anna, but also removed her memories of Elsa having powers over ice and snow. He said that fear would be her enemy, and so her mother and father grew fearful. They locked the gates and limited Elsa's contact with people.

Personally, I don't think they should have locked the gates and limited Elsa's contact with people. Locked up inside her room with no other person to talk to except her parents could be traumatizing. Elsa lived almost her whole life in fear of having no control over her powers, which only made them harder to control. Plus Elsa's emotions were negative ones, in which her powers are connected to her emotions, it made it harder to control.
I think it's most likely that the King taught Elsa to just ignore her powers, because of the statement, "Conceal, don't feel, don't let them know." Obviously he taught her not to feel that she had powers, like they weren't there so that she wouldn't feel so isolated. It seems to me that Elsa just ignored her emotions, in order not to let her powers to be unleashed. But it only made it harder to control, because her powers are connected to her emotions. And with lack of experience with dealing with her emotions, she couldn't control it.

I think that they should have exposed to Elsa to people so that she could deal with her emotions, because, like I've said numerous times in this article, her powers are directly linked to her emotions. She's lived in fear all her life, almost never feeling happiness, which is just said and traumatizing.

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Okay! That's the end of my article. I hoped you enjoyed it. This is just my opinion so you can just share what you think of this article/subject in the comments. They're gladly accepted.
Have a nice day~ :)