Geometric Brownian Motion unable to model / predict jumps

In my finance course, we were talking about the flaws of modelling Stock Prices with the geometric Brownian Motion. According to my professor:

"Since the geometric Brownian Motion has continous time sample path, it does not allow for jumps in its values when rare events occur"

I fail to really understand this explication for the no-jump problem. If we take a look at the log normal distribution of the prices, then there should be the small possibility of an "extreme change", resp. a very rare event occurring and therefore experiencing a jump?

If anyone has a more detailed explanation than just the quote above, I would be very thankful

Assume that the value of the sample path of the geometric Brownian motion equals $$10$$ at time $$t_0$$ and equals 100 at time $$t_0 + \Delta t$$. For the value to change from $$10$$ to $$100$$, the path should necessarily go over all the values between $$10$$ and $$100$$ (possibly with fluctuations) during the intermediate time $$\Delta t$$; it cannot jump directly from $$10$$ to $$100$$.
On the other hand, if we consider a process with jumps, then it is possible for it to be $$10$$ at time $$t_0$$ and jump to $$100$$ after a very small (infinitesimal) amount of time $$\Delta t$$. This jump will create a gap on the plot of the sample path and may indicate some rare event.