FFF, were you VFR or IFR?
Another thing to consider; you state that you were a training flight. Perhaps because of that very fact the ATCO didn't want to do something 'non-standard' such as....
and given radar vectors to take me away from his climb-out
Even then, ATC has to provide IFR/SVFR separation based on speed groups for departing aircraft. Even with more than a 45 degree turn away from the track of the departing 737, it might have been two or three minutes before ATC could release it. Or perhaps the 737 was going the same way as you, and Tower didn't think you'd like to turn away from your intedned route? Or maybe it was feasible, but there was a trainee on Radar and Tower didn't want to overload him/her. Lots of possiblities besides basic flight priorities. 