The short answer why C2 and C3 are not stereocenters is, Because C2 and C3 can’t make stereoisomers by swapping the position of substituents connected to them.
More detailed explanation
What is stereocenter?
The stereocenter is any atom that can make different isomers by swapping the position of connected substituent groups or atoms.
It can be any atom (carbon is most common).
The hybridization can be either sp2 or sp3 but not sp.
The substituents need to be all different atom or group whether they are sp2 or sp3.
It can have a double bond.
It can be chiral or achiral.
Stereocenter Example
Let’s look at an example. If you look at carbon 4 (C4) and 5 (C5), their connection of substituents can be simplified like this.
Now swap the position of hydrogen and R2 on carbon 4 (C4). They become stereoisomers E and Z. The same results can be achieved by swapping Cl and R1 on C5. If you look at C4 and C5 individually, they meet the above criteria. Therefore, C4 and C5 are stereocenters.
Now, let’s look at C2 and C3. Simplify the connection of substituents of C2 and C3 the same way we did before.
Now C2 is connected to 2 methyl groups (-CH3). Swapping the position of these 2 methyl groups won’t make different isomers. It will be the identical molecule before and after swapping. The same thing can be said to C3. Swapping the position of R3 and H will still make the identical molecule and won’t make isomers. Therefore, C2 and C3 are not stereocenters.