Why do they stage after surgery ?

Pathology is not final until the complete mass is removed, and true sizing is not known until after surgery, so since stage is based on location of the mass, size of the mass, and number of positive nodes it is not usually done until after surgery.  Also, there is clinical staging - which is the estimated stage based on biopsy and imaging, and pathological stage which is based on post-surgical information.  Imaging is not 100% accurate, and a biopsy sample does not necessarily show the complete picture as it is a small part of the tumor and tumors are not homogenous throughout.  When final pathology is done they look at many slices of the tumor and do a more thorough assessment.  1/4 nodes means that out of four nodes removed, one was positive for cancer.  In a sentinel node biopsy all the nodes that are designated by the dye and/or tracer are removed - sometimes that is one, sometimes more.  Also the nodes are encased in a fat pad - often they are clumped, or what initially appears to be one is actually more.

Edited to add:  Annette and I must have been cross typing, lol!  She had a more succinct answer!

They stage after surgery because that's when the pathologists have the full package to study, i.e., both the tumor itself and the surrounding tissue (including margins). The biopsy only samples a very small portion of the suspicious area,which is also why the biopsy path report sometimes ends up differing from the surgical path report.

When they excise nodes, they identify how many how many of the nodes were taken had cancer cells in them/how many nodes were taken out in all--hence, 1/4 in your example = 1 cancerous node/out of 4 nodes excised.

You might want to use the information tools at the bco site, where you can get full, professional explanations of the many new terms you will be getting to learn. (This section is in the red line at the head of the bco main website (Diagnosis, Treatments, etc.)

As you have been told Stage can not be determined until after surgery. There are many variables though - including the type. Neoadjuvant Chemo (Chemo before surgery) will effect what is present at surgery but not show what was originally there. For some, neoadjuvant is a must before surgery. For some neoadjuvant and adjuvant (Chemo after surgery) are what is needed. Nothing is 'cut and dried' as absolute.