Did the METAR come from your own field, or another? If so, how far away? Just because it was 7kts one minute, doesn't mean you won't get veering shear and an increase the next.
The TAF forecast 16kts right on the beam (300 - 230 = 70 deg.) Yes, it may have been OK for an instructor, but you may have done a short flight and then got completely caught out.
Having said that, I don't know what your status is (hours/stude et al).
Lightish winds not as forecast is... sod's law. A meaningful discussion with the one who made the decision is often beneficial to learn why people make the decisions they do.