This seems to boil down to four main elements;
1) Grand Pabbie's info was quite vague. His general advice was that she needs to control her powers. Her parents take this to mean that she should restrain them rather than learning to use them effectively.
2) Elsa is seen by her parents as being a danger to herself and others. Arguably, when she does take the gloves off (both metaphorically and literally) she almost kills the entire kingdom.
3) Elsa's magical abilities are growing and becoming more uncontrollable over time. Her parents seem deeply worried that if the Kingdom find out about her powers, that they'll react with fear and loathing, harming her chances of becoming the next Queen.
The king and queen acted just as cautiously inside the castle. As the princesses grew, their parents did everything they could to ensure that Elsa learned to control herself. That meant the girls were hardly ever together. Nor did Elsa seek Anna out, since she was afraid she might accidentally hurt her. Day after day, Elsa spent most of her time training to be the next ruler—and learning to keep her powers in check.
The training was difficult, and Elsa often felt unable to contain her magic. Ice seemed to form on her fingertips whenever she laughed or cried or became upset.
Worried, the king gave Elsa a pair of leather gloves. He advised her to keep them on at all times, and reminded her that she had to hide her icy magic in order to stay safe. “Conceal it,” he told her.
“Don’t feel it,” she answered.
“Don’t let it show,” he agreed.
Frozen: The Junior Novelisation
Elsa herself is unwilling to use her magic constructively. Her fear is that she will cause harm to others. She simply wants to repress her powers.
Without any memory of Elsa’s magic, Anna had no idea why she was
always alone. Over time, she simply came to accept that her sister’s
coldness was part of who she was. She didn’t know that Elsa was lonely
too, and that she missed Anna as much as Anna missed her. Elsa longed
to play with Anna but was fearful of the harm her magic might cause by
mistake.
Frozen: The Junior Novelisation