The consumer price index is definitely flawed. However, one thing I've heard is that the massive drop in demand and velocity of money is necessary to consider when analyzing inflation. I also was initially worried about inflation given the massive stimulus numbers we're seeing but have been reconsidering this.
I'm not well-versed in this at all, but demand-pull inflation under Keynesian economics [1] or a drop in V (velocity of money) in the equation of exchange in the monetarist theory of money [2] seem to be what is supporting why folks are worried about deflation. I would venture to guess that this is part of why the Fed is doing these massive buys right now, too.
Tangentially, pointers to good econ learning resources from anyone would be helpful. I've only started with Khan Academy and what I remember from old classes so far.
[0] https://fred.stlouisfed.org/graph/?g=qH1p [1] https://en.wikipedia.org/wiki/Inflation#Keynesian_view [2] https://en.wikipedia.org/wiki/Inflation#Monetarist_view