If a lymph node is very soft and very moveable but 2.5 cm and never grows is it cancerous?

Infections: The fact there is a positive respose to antibiotics certainly entertains the possiblity of chronic infections but any adenopathy not resolving and on both sides of body as well as upper and lower body needs an evaluation with a complete inectious workup, lymphoma workup and probable biopsy . There are many condition both serious and benign that could be the cause please seek medical evaluation.

Possibly: It is difficult to know for sure. There are many reasons a lymph node can enlarge such as infection, inflammation and also cancer. Not all cancerous lymph nodes are hard and some diseases like low grade lymphomas can stay at the same size for a long time. You shoud see a doctor to have it examined.

Biopsy needed: You will never know. Lymph node enlargement can be caused by infection vs inflammation vs cancer. It is possibly benign however, the only and the best way to find out whether it is benign or cancerous is by having a biopsy done on the affected lymph node. A biopsy should probably be done/considered to be done to any lymph node bigger than 2 CM to really rule out malignancy.