Unless they have done an ultrasound and mammogram and have real suspicion (in my case, the ultrasound was highly suspicious for malignancy), sometimes they do recommend removing it. In my case, the surgeon said even if it was a fibroadenoma, they needed to remove it. The fact that they are skipping the core needle biopsy means nothing at this time. And moveable does not mean that it is loose and can slide around the breast, but they see if it feels attached as a mass. Whether it is moveable is just one thing they look at,....moveable is a better sign, but cannot diagnose a lumo just by touch.
Kudos to your doc for sending you for more tests. Hang in there,...the waiting is really hard, we know.