Sometimes the anime does it to give the protagonist freedom. So they don't have parents telling them not to do something. Or, in some cases, stopping them. Especially in any anime where fighting or combat will be involved as the inherent danger would make a parent balk at sending their child. Or in any kind of harem anime where the main character will find themselves in "questionable" circumstances.
Alternatively, they take the parents out of the equation because otherwise they would do whatever the main would. I mean would you rather a 14 year old saving the world or the 36 year old parent who maybe has some actual life skills. (EX- Navy Seal Dad versus bad guys instead of kid vs bad guys.)