What is biological intuition?
This is how I understand it: Bioinformatics tools are amazing at answering questions. The more specific the question each individual module of a tool can answer, the better their quality.

However, what they cannot do is ask the right question. You can find motifs with scores attached to the hit, but you cannot predict the relevance of that find. Is it a motif for a transcription factor binding site that inhibits a promoter for a downstream gene thereby suppressing activity, or does it bind a different factor enhancing a gene further downstream?

These questions need knowledge of the domain and of the genomic context, and this knowledge base is constantly evolving. Tools are getting intelligent, but they cannot have this intuition because they are still designed my human beings and we are always ahead thanks to experience.