There are many good reasons to use a symmetric probability distribution when modelling a problem:

1. Simplicity: Symmetric distributions are often simpler and easier to work with mathematically than more complex, asymmetric distributions.
2. No skewness: If there is no skewness in the data, then using a symmetric distribution can be appropriate. For example, if the data is normally distributed, a symmetric distribution is a good fit.
3. Unknown distribution: If the distribution of the data is unknown, a symmetric distribution can be a reasonable starting point for analysis. This is because symmetric distributions are relatively easy to estimate and test for goodness of fit.
4. Comparison: Using a symmetric distribution allows for easy comparison with other data sets that are also modelled using symmetric distributions. This can be useful in certain contexts, such as in financial markets or in comparing different populations.
5. Balanced outcome: When the outcome of interest is equally likely to occur on both sides of the mean, a symmetric distribution can be an appropriate choice. For example, when modelling the distribution of test scores for a fair exam, a symmetric distribution may be a good choice.
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