Handwaving
The term "handwaving" is used in mathematics and physics to describe arguments that are not mathematically rigorous.Such arguments often include order-of-magnitude estimates and appeals to symmetry or dimensional consistency. Competent researchers and professors rely on handwaving when, given a limited time, a large result must be shown and minor technical details cannot be given much attention (e.g. "it can be shown that x is even").
The term derives from the use of gestures to add emphasis when stating arguments, and the tendency to continue or increase the gesturing as a substitute for mathematics, when an argument is hard to put across or the proponent is tired of deploying words and/or symbols.
The expression "vigorous handwaving" is meant to suggest at least that the proponent should be aware of failing to convince; it may suggest the proponent lacks confidence in the validity of their own argument.