A parameter can be thought of as a constant variable. It is a variable for which you determine a value, or whose value you change to see its effects on the situation modeled. The term is used in Geometry, Statistics, Physics and Engineering nas well as other fields.
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Because it varies, otherwise it would be a constant.
The constant is the number; the variable is the letter.
The question is about an oxymoronic expression. A constant cannot be a variable and a variable cannot be a constant!
Constant variable
The opposite of the word "constant" is "variable".