Why did our doctor recommend radiation when our 1st psa is 0.02 after prostatotomy?

Positive margin. Most likely reason is adverse factors at the time of pathology review, like positive margins. This is an indication for adjuvant radiation. Giving radiation soon after surgery once urination has been optimized to improve outcome. This is different than salvage radiation given when there is evidence of rise of psa post surgery.
Tumor still there. After surgery, if the psa didn't drop to 0, good chance that not all tumor was removed. Ask your doctor if there were any positive margins during surgery.
Potential residual. If all prostate tissue has been removed, the psa should typically drop to <0.01. However, the main question right now is whether the residual psa is due to just residual normal prostate cells, or prostate cancer cells. One option is to just repeat in a few months and see - if it's rising, we think that's more likely due to cancer growth. If it stays steady, can be ok to keep monitoring.
Ask your doctor why? Each case is different and it may be because there are a lot of the margins that are posiitve. However a positive margin is not an absolute need for radiation. If the psa is rising after prostatectomy you can watch and as long as you treat before it goes over 1.0 good results can be obtained. A lot of urologist are beginning to own radiation centers and you are right to question the motives.
Psa and radiation. It usually is interpreted as indicating that there is some cancer left behind if the psa does not fall to zero after prostatectomy. Radiation is more successful if it is given before the psa rises above about 0.2.
PSA post RPA. Because it is supposed to be zero after surgery, and the presence of any psa indicated residual...Prostate or cancer, and if it was 0, and rising, growing cancer. Some call this adjuvant; i'd call it salvage. Usualy w wait to optimize continence and erectile function.
ProstateBed at risk. After prostatectomy, the psa should go very close to zero and remained there. Post-prostatectomy radiation is recommended at the first rise of psa or when there is adverse features at the time of prostatectomy/pathology review. Those indications may be positive surgical margin, extracapsular extension, perineural invasion etc., i assume in your case, there may have been adverse features.