I strongly disagree with the statement saying that "At school, students should only study what they enjoy".

strongly 是形容词 strong 的副词形式，由 strong（"强壮的、强烈的"）加后缀 -ly 构成，表示"强烈地、坚决地"的意思。在这里修饰动词 disagree，表示"强烈不同意"。