Perhaps one of the best arguments supporting RT in breast cancer is the not-that-often cited Scottish Trial that randomized women to postoperative RT or chemotherapy following breast conservation; the breast failure rate following adjuvant chemotherapy alone approximated 30% with short follow-up. Ob...

The answer has to do with tumor burden. Chemotherapy (or other systemic therapy) has the advantage of widespread distribution but generally is most effective against small numbers of malignant cells. Clinically apparent disease usually requires surgical removal (if feasible) but often radiotherapy a...

You can also answer from your own experience with examples. Patients (especially like her with TNBC) who rejected adjuvant radiation therapy, even those with ypT0 N0, recurred and suffered needlessly. The radiation risks are minimal yet the benefits for certain individuals can be enormous -- a patie...

I love analogies for explaining, and I really dig into the "broken glass" analogy in this case. It is akin to the "weeds" analogy mentioned in another comment. For patients who are receiving trimodality, I say something like this: "Breast cancer is like dropping a glass on the floor. It breaks and ...

You can say, "Outside of surgery, radiation packs the greatest punch locally for potential microscopic residual disease and improving local control. This is a potential disease too small for even the best surgeon to see with the naked eye." 

I think this is a very difficult question to answer from a data standpoint.The triple negativity in your patient may be the most reasonable argument to offer radiation. A review by Jordana de Faria Bessa & Gustavo Nader Marta supporting that can be found here.