Songs and poems becoming part of children's lives is not liked by parents because through this children—

The passage clearly states that parents fear children may stray from the path on which the parents want to lead them, meaning they may not reach the destination/goal that parents have set for them. The mother feels that if children get absorbed in songs and poems, they will deviate from the route the parents have planned. Hence the concern is specifically about not achieving the parent-determined goal, not merely about studies or enjoyment in general.