TWayne wrote:

....

A 40" fan has to have a pretty good sized motor and takes several
seconds for it to come up to speed. Everything being reactive, while it
is starting, it is creating reverse EMF (electro-motive-force) which,
during that time, is making the current in the two feed wires go out of
phase with each other.
B.S. Unless you have a very big reservoir for electrons, the current
on the two feed wires will not be "out of phase".
A large capacitor to ground would be such a reservoir, but that is
a ground fault, and the GFCI should trip for that.

....
If it still pops, you could try VERY CAREFULLY (ELECTRICITY CAN
*KILL* YOU) TRY shorting around the GFCI with a lead until the fan gets
running. Then remove the bypass; If the fan continues to run, there is
there is no problem with the fan.
Not necessarily. There may be both mechanical and electrical
differences in the motor during acceleration that could cause
a ground fault during acceleration. OP didn't mention whether
this motor had a centrifugal switch controlling the start winding.

Most likely you have a ground fault in the motor.
It may be solid or it may be intermittent.
Have you tried measuring the resistance from hot to ground
for the motor?