On the face of it, you’d think that growing up in a household populated by writers would be a real benefit for a young, developing writer. I’ve seen this to be true, not so true, and both.
The benefits of having writing parents include exposure to more reading and discussing of books than occurs in other homes. A love and talent for expressing the written word gets into the blood from an early age. In addition, if a child’s primary role models are leading a life that includes writing, the child learns that this is a valid direction in life to consider.
The darker possibilities of having writer parent(s) is that they may have blocks and problems with their writing that generate negative patterns and associations with writing. Perhaps they also focus on their work so much they ignore basic parenting duties like feeding their children. They may also have too much invested in the child’s writing, and be overly involved or judgmental.
Another brutal reality is that if a parent’s writing career has been less than stellar, they may not truly want their offspring to enjoy literary success, and will communicate this directly or indirectly.
None of us escape childhood without a few or several emotional issues to contend with in adult life, and these issues may intersect with the writing process. If things are not going well with your writing, you may have to look at the beliefs and feelings about writing that you carry. If you grew up with family members who wrote, do some reflection on their writing process, and how they communicated to you about writing. There might be something useful to understand there.