In general, it's safest to use the same passport for any given country until that passport expires. If it's necessary to switch for any given country, it's best to switch while you're outside that country unless you reside in the country.
Someone with multiple nationalities must choose which nationality to use. The choice of nationality may or may not be free: some countries require their citizens to present themselves as such to border authorities. Similarly, someone with a right of permanent or temporary residence in a country may be constrained to a particular nationality when dealing with that country's border authorities.
In this case, the person is a dual national of the country in question, but used her foreign passport to leave that country. There is another general rule that applies to this case, which is that countries must generally admit their own citizens. Therefore, someone in this position should generally be allowed to enter her country of nationality with that country's passport, regardless of the documents she used leaving the country.
However, I do not know Egypt's stance on dual nationality. Perhaps she violated some law by leaving with her US passport, and perhaps returning with an Egyptian passport would expose her to a fine or other punishment, or to loss of Egyptian nationality. There may be other specific considerations that make it inadvisable to use her Egyptian passport.